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ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - start with the Axiom of Extensionality
Classes
Class equality
eqcomi
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neqcomd
Metamath Proof Explorer
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Theorem
eqcomi
Description:
Inference from commutative law for class equality.
(Contributed by
NM
, 26-May-1993)
Ref
Expression
Hypothesis
eqcomi.1
⊢
A
=
B
Assertion
eqcomi
⊢
B
=
A
Proof
Step
Hyp
Ref
Expression
1
eqcomi.1
⊢
A
=
B
2
eqcom
⊢
A
=
B
↔
B
=
A
3
1
2
mpbi
⊢
B
=
A