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Theorem cdeqnot 2817
Description: Distribute conditional equality over negation. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
cdeqnot.1  |- CondEq ( x  =  y  ->  ( ph 
<->  ps ) )
Assertion
Ref Expression
cdeqnot  |- CondEq ( x  =  y  ->  ( -.  ph  <->  -.  ps )
)

Proof of Theorem cdeqnot
StepHypRef Expression
1 cdeqnot.1 . . . 4  |- CondEq ( x  =  y  ->  ( ph 
<->  ps ) )
21cdeqri 2815 . . 3  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
32notbid 625 . 2  |-  ( x  =  y  ->  ( -.  ph  <->  -.  ps )
)
43cdeqi 2814 1  |- CondEq ( x  =  y  ->  ( -.  ph  <->  -.  ps )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 103  CondEqwcdeq 2812
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578
This theorem depends on definitions:  df-bi 115  df-cdeq 2813
This theorem is referenced by: (None)
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