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Theorem cdeqi 2743
Description: Deduce conditional equality. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
cdeqi.1 (x = yφ)
Assertion
Ref Expression
cdeqi CondEq(x = yφ)

Proof of Theorem cdeqi
StepHypRef Expression
1 cdeqi.1 . 2 (x = yφ)
2 df-cdeq 2742 . 2 (CondEq(x = yφ) ↔ (x = yφ))
31, 2mpbir 134 1 CondEq(x = yφ)
Colors of variables: wff set class
Syntax hints:  wi 4  CondEqwcdeq 2741
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110  df-cdeq 2742
This theorem is referenced by:  cdeqth  2745  cdeqnot  2746  cdeqal  2747  cdeqab  2748  cdeqim  2751  cdeqcv  2752  cdeqeq  2753  cdeqel  2754
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