Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - start with the Axiom of Extensionality
Power classes
pweqi
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pweqd
Metamath Proof Explorer
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Theorem
pweqi
Description:
Equality inference for power class.
(Contributed by
NM
, 27-Nov-2013)
Ref
Expression
Hypothesis
pweqi.1
⊢
A
=
B
Assertion
pweqi
⊢
𝒫
A
=
𝒫
B
Proof
Step
Hyp
Ref
Expression
1
pweqi.1
⊢
A
=
B
2
pweq
⊢
A
=
B
→
𝒫
A
=
𝒫
B
3
1
2
ax-mp
⊢
𝒫
A
=
𝒫
B