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Theorem cdeqri 2815
Description: Property of conditional equality. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
cdeqri.1  |- CondEq ( x  =  y  ->  ph )
Assertion
Ref Expression
cdeqri  |-  ( x  =  y  ->  ph )

Proof of Theorem cdeqri
StepHypRef Expression
1 cdeqri.1 . 2  |- CondEq ( x  =  y  ->  ph )
2 df-cdeq 2813 . 2  |-  (CondEq (
x  =  y  ->  ph )  <->  ( x  =  y  ->  ph ) )
31, 2mpbi 143 1  |-  ( x  =  y  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4  CondEqwcdeq 2812
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104
This theorem depends on definitions:  df-bi 115  df-cdeq 2813
This theorem is referenced by:  cdeqnot  2817  cdeqal  2818  cdeqab  2819  cdeqal1  2820  cdeqab1  2821  cdeqim  2822  cdeqeq  2824  cdeqel  2825  nfcdeq  2826
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