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Theorem cdeqri 2946
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 2944 . 2  |-  (CondEq (
x  =  y  ->  ph )  <->  ( x  =  y  ->  ph ) )
31, 2mpbi 145 1  |-  ( x  =  y  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4  CondEqwcdeq 2943
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106
This theorem depends on definitions:  df-bi 117  df-cdeq 2944
This theorem is referenced by:  cdeqnot  2948  cdeqal  2949  cdeqab  2950  cdeqal1  2951  cdeqab1  2952  cdeqim  2953  cdeqeq  2955  cdeqel  2956  nfcdeq  2957
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