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Theorem cdeqnot 2979
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 2977 . . 3  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
32notbid 285 . 2  |-  ( x  =  y  ->  ( -.  ph  <->  -.  ps )
)
43cdeqi 2976 1  |- CondEq ( x  =  y  ->  ( -.  ph  <->  -.  ps )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176    = wceq 1623  CondEqwcdeq 2974
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 2975
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