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ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - start with the Axiom of Extensionality
Conditional equality (experimental)
cdeqi
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cdeqri
Metamath Proof Explorer
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Theorem
cdeqi
Description:
Deduce conditional equality.
(Contributed by
Mario Carneiro
, 11-Aug-2016)
Ref
Expression
Hypothesis
cdeqi.1
⊢
x
=
y
→
φ
Assertion
cdeqi
⊢
CondEq
x
=
y
→
φ
Proof
Step
Hyp
Ref
Expression
1
cdeqi.1
⊢
x
=
y
→
φ
2
df-cdeq
⊢
CondEq
x
=
y
→
φ
↔
x
=
y
→
φ
3
1
2
mpbir
⊢
CondEq
x
=
y
→
φ