diff --git a/src/constraints.jl b/src/constraints.jl
index b42ea4495ca..5db80f7ca12 100644
--- a/src/constraints.jl
+++ b/src/constraints.jl
@@ -1543,18 +1543,31 @@ function relax_with_penalty!(
     return relax_with_penalty!(model, Dict(); default = default)
 end
 
-struct _BooleanEqualTo end
+struct _DoNotConvertSet{S} <: MOI.AbstractScalarSet
+    set::S
+end
+
+model_convert(::AbstractModel, set::_DoNotConvertSet) = set
+
+function moi_set(constraint::ScalarConstraint{F,<:_DoNotConvertSet}) where {F}
+    return constraint.set.set
+end
+
+function _build_boolean_equal_to(::Function, lhs, rhs)
+    set = _DoNotConvertSet(MOI.EqualTo(true))
+    return ScalarConstraint(op_equal_to(lhs, rhs), set)
+end
 
-function build_constraint(::Function, lhs, rhs, ::_BooleanEqualTo)
-    return ScalarConstraint(op_equal_to(lhs, rhs), MOI.EqualTo(true))
+function _build_boolean_equal_to(::Function, lhs::Bool, rhs)
+    return ScalarConstraint(rhs, _DoNotConvertSet(MOI.EqualTo(lhs)))
 end
 
-function build_constraint(::Function, lhs::Bool, rhs, ::_BooleanEqualTo)
-    return ScalarConstraint(rhs, MOI.EqualTo(lhs))
+function _build_boolean_equal_to(::Function, lhs, rhs::Bool)
+    return ScalarConstraint(lhs, _DoNotConvertSet(MOI.EqualTo(rhs)))
 end
 
-function build_constraint(::Function, lhs, rhs::Bool, ::_BooleanEqualTo)
-    return ScalarConstraint(lhs, MOI.EqualTo(rhs))
+function _build_boolean_equal_to(error_fn::Function, lhs::Bool, rhs::Bool)
+    return error_fn("cannot add the trivial constraint `$lhs := $rhs`")
 end
 
 function parse_constraint_head(error_fn::Function, ::Val{:(:=)}, lhs, rhs)
@@ -1564,8 +1577,6 @@ function parse_constraint_head(error_fn::Function, ::Val{:(:=)}, lhs, rhs)
         $parse_code_lhs
         $parse_code_rhs
     end
-    build_code = quote
-        build_constraint($error_fn, $new_lhs, $new_rhs, _BooleanEqualTo())
-    end
+    build_code = :(_build_boolean_equal_to($error_fn, $new_lhs, $new_rhs))
     return false, parse_code, build_code
 end
diff --git a/src/macros.jl b/src/macros.jl
index 2a5127bfc34..9cb281d0315 100644
--- a/src/macros.jl
+++ b/src/macros.jl
@@ -1160,10 +1160,6 @@ function model_convert(model::AbstractModel, set::MOI.AbstractScalarSet)
     return set
 end
 
-function model_convert(model::GenericModel{Bool}, set::MOI.EqualTo{Bool})
-    return set
-end
-
 function model_convert(model::AbstractModel, α::Number)
     T = value_type(typeof(model))
     V = variable_ref_type(model)
diff --git a/test/test_constraint.jl b/test/test_constraint.jl
index 98a0ce4e3b0..02e5dd009e8 100644
--- a/test/test_constraint.jl
+++ b/test/test_constraint.jl
@@ -1766,34 +1766,34 @@ function test_def_equal_to_operator_float()
     c = @constraint(model, x[1] := x[2])
     o = constraint_object(c)
     @test isequal_canonical(o.func, op_equal_to(x[1], x[2]))
-    @test o.set == MOI.EqualTo(1.0)
+    @test o.set == MOI.EqualTo(true)
     # x[1] == x[2] := false
     c = @constraint(model, x[1] == x[2] := false)
     o = constraint_object(c)
     @test isequal_canonical(o.func, op_equal_to(x[1], x[2]))
-    @test o.set == MOI.EqualTo(0.0)
+    @test o.set == MOI.EqualTo(false)
     # x[1] && x[2] := false
     c = @constraint(model, x[1] && x[2] := false)
     o = constraint_object(c)
     @test isequal_canonical(o.func, op_and(x[1], x[2]))
-    @test o.set == MOI.EqualTo(0.0)
+    @test o.set == MOI.EqualTo(false)
     # x[1] && x[2] := true
     c = @constraint(model, x[1] && x[2] := true)
     o = constraint_object(c)
     @test isequal_canonical(o.func, op_and(x[1], x[2]))
-    @test o.set == MOI.EqualTo(1.0)
+    @test o.set == MOI.EqualTo(true)
     # x[1] || x[2] := y
     y = true
     c = @constraint(model, x[1] || x[2] := y)
     o = constraint_object(c)
     @test isequal_canonical(o.func, op_or(x[1], x[2]))
-    @test o.set == MOI.EqualTo(1.0)
+    @test o.set == MOI.EqualTo(true)
     # y := x[1] || x[2]
     y = true
     c = @constraint(model, y := x[1] || x[2])
     o = constraint_object(c)
     @test isequal_canonical(o.func, op_or(x[1], x[2]))
-    @test o.set == MOI.EqualTo(1.0)
+    @test o.set == MOI.EqualTo(true)
     return
 end