Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - start with the Axiom of Extensionality
Classes
Class equality
eqeq1i
Next ⟩
eqcomd
Metamath Proof Explorer
Ascii
Unicode
Theorem
eqeq1i
Description:
Inference from equality to equivalence of equalities.
(Contributed by
NM
, 15-Jul-1993)
Ref
Expression
Hypothesis
eqeq1i.1
⊢
A
=
B
Assertion
eqeq1i
⊢
A
=
C
↔
B
=
C
Proof
Step
Hyp
Ref
Expression
1
eqeq1i.1
⊢
A
=
B
2
eqeq1
⊢
A
=
B
→
A
=
C
↔
B
=
C
3
1
2
ax-mp
⊢
A
=
C
↔
B
=
C