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Theorem niabn 952
Description: Miscellaneous inference relating falsehoods. (Contributed by NM, 31-Mar-1994.)
Hypothesis
Ref Expression
niabn.1  |-  ph
Assertion
Ref Expression
niabn  |-  ( -. 
ps  ->  ( ( ch 
/\  ps )  <->  -.  ph )
)

Proof of Theorem niabn
StepHypRef Expression
1 simpr 109 . 2  |-  ( ( ch  /\  ps )  ->  ps )
2 niabn.1 . . 3  |-  ph
32pm2.24i 613 . 2  |-  ( -. 
ph  ->  ps )
41, 3pm5.21ni 693 1  |-  ( -. 
ps  ->  ( ( ch 
/\  ps )  <->  -.  ph )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 103    <-> wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  ninba  957
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