Database
SUPPLEMENTARY MATERIAL (USERS' MATHBOXES)
Mathbox for BJ
Set theory
Tuples of classes
bj-projex
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bj-projval
Metamath Proof Explorer
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Theorem
bj-projex
Description:
Sethood of the class projection.
(Contributed by
BJ
, 6-Apr-2019)
Ref
Expression
Assertion
bj-projex
⊢
B
∈
V
→
A
Proj
B
∈
V
Proof
Step
Hyp
Ref
Expression
1
df-bj-proj
⊢
A
Proj
B
=
x
|
x
∈
B
A
2
bj-clex
⊢
B
∈
V
→
x
|
x
∈
B
A
∈
V
3
1
2
eqeltrid
⊢
B
∈
V
→
A
Proj
B
∈
V