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Theorem cdeqi 2801
Description: Deduce conditional equality. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
cdeqi.1  |-  ( x  =  y  ->  ph )
Assertion
Ref Expression
cdeqi  |- CondEq ( x  =  y  ->  ph )

Proof of Theorem cdeqi
StepHypRef Expression
1 cdeqi.1 . 2  |-  ( x  =  y  ->  ph )
2 df-cdeq 2800 . 2  |-  (CondEq (
x  =  y  ->  ph )  <->  ( x  =  y  ->  ph ) )
31, 2mpbir 144 1  |- CondEq ( x  =  y  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4  CondEqwcdeq 2799
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-cdeq 2800
This theorem is referenced by:  cdeqth  2803  cdeqnot  2804  cdeqal  2805  cdeqab  2806  cdeqim  2809  cdeqcv  2810  cdeqeq  2811  cdeqel  2812
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