Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - start with the Axiom of Extensionality
Binary relations
breq1i
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breq2i
Metamath Proof Explorer
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Unicode
Theorem
breq1i
Description:
Equality inference for a binary relation.
(Contributed by
NM
, 8-Feb-1996)
Ref
Expression
Hypothesis
breq1i.1
⊢
A
=
B
Assertion
breq1i
⊢
A
R
C
↔
B
R
C
Proof
Step
Hyp
Ref
Expression
1
breq1i.1
⊢
A
=
B
2
breq1
⊢
A
=
B
→
A
R
C
↔
B
R
C
3
1
2
ax-mp
⊢
A
R
C
↔
B
R
C