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Theorem cdeqri 3011
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 3009 . 2  |-  (CondEq (
x  =  y  ->  ph )  <->  ( x  =  y  ->  ph ) )
31, 2mpbi 199 1  |-  ( x  =  y  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1633  CondEqwcdeq 3008
This theorem is referenced by:  cdeqnot  3013  cdeqal  3014  cdeqab  3015  cdeqal1  3016  cdeqab1  3017  cdeqim  3018  cdeqeq  3020  cdeqel  3021  nfcdeq  3022
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-cdeq 3009
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