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ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - start with the Axiom of Extensionality
Classes
Class equality
eqeq2i
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eqeqan12d
Metamath Proof Explorer
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Theorem
eqeq2i
Description:
Inference from equality to equivalence of equalities.
(Contributed by
NM
, 26-May-1993)
Ref
Expression
Hypothesis
eqeq2i.1
⊢
A
=
B
Assertion
eqeq2i
⊢
C
=
A
↔
C
=
B
Proof
Step
Hyp
Ref
Expression
1
eqeq2i.1
⊢
A
=
B
2
eqeq2
⊢
A
=
B
→
C
=
A
↔
C
=
B
3
1
2
ax-mp
⊢
C
=
A
↔
C
=
B