Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - start with the Axiom of Extensionality
Unordered and ordered pairs
opeq1i
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opeq2i
Metamath Proof Explorer
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Theorem
opeq1i
Description:
Equality inference for ordered pairs.
(Contributed by
NM
, 16-Dec-2006)
Ref
Expression
Hypothesis
opeq1i.1
⊢
A
=
B
Assertion
opeq1i
⊢
A
C
=
B
C
Proof
Step
Hyp
Ref
Expression
1
opeq1i.1
⊢
A
=
B
2
opeq1
⊢
A
=
B
→
A
C
=
B
C
3
1
2
ax-mp
⊢
A
C
=
B
C