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Theorem ninba 927
Description: Miscellaneous inference relating falsehoods. (Contributed by NM, 31-Mar-1994.)
Hypothesis
Ref Expression
ninba.1  |-  ph
Assertion
Ref Expression
ninba  |-  ( -. 
ps  ->  ( -.  ph  <->  ( ch  /\  ps )
) )

Proof of Theorem ninba
StepHypRef Expression
1 ninba.1 . . 3  |-  ph
21niabn 917 . 2  |-  ( -. 
ps  ->  ( ( ch 
/\  ps )  <->  -.  ph )
)
32bicomd 192 1  |-  ( -. 
ps  ->  ( -.  ph  <->  ( ch  /\  ps )
) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 176    /\ wa 358
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-an 360
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