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Theorem cdeqth 2813
Description: Deduce conditional equality from a theorem. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
cdeqth.1  |-  ph
Assertion
Ref Expression
cdeqth  |- CondEq ( x  =  y  ->  ph )

Proof of Theorem cdeqth
StepHypRef Expression
1 cdeqth.1 . . 3  |-  ph
21a1i 9 . 2  |-  ( x  =  y  ->  ph )
32cdeqi 2811 1  |- CondEq ( x  =  y  ->  ph )
Colors of variables: wff set class
Syntax hints:  CondEqwcdeq 2809
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 2810
This theorem is referenced by:  cdeqal1  2817  cdeqab1  2818  nfccdeq  2824
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