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bj-pr2ex
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Theorem
bj-pr2ex
Description:
Sethood of the second projection.
(Contributed by
BJ
, 6-Oct-2018)
Ref
Expression
Assertion
bj-pr2ex
⊢
A
∈
V
→
pr2
A
∈
V
Proof
Step
Hyp
Ref
Expression
1
df-bj-pr2
⊢
pr2
A
=
1
𝑜
Proj
A
2
bj-projex
⊢
A
∈
V
→
1
𝑜
Proj
A
∈
V
3
1
2
eqeltrid
⊢
A
∈
V
→
pr2
A
∈
V