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Theorem 2falsed 618
Description: Two falsehoods are equivalent (deduction rule). (Contributed by NM, 11-Oct-2013.)
Hypotheses
Ref Expression
2falsed.1  |-  ( ph  ->  -.  ps )
2falsed.2  |-  ( ph  ->  -.  ch )
Assertion
Ref Expression
2falsed  |-  ( ph  ->  ( ps  <->  ch )
)

Proof of Theorem 2falsed
StepHypRef Expression
1 2falsed.1 . . 3  |-  ( ph  ->  -.  ps )
21pm2.21d 549 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
3 2falsed.2 . . 3  |-  ( ph  ->  -.  ch )
43pm2.21d 549 . 2  |-  ( ph  ->  ( ch  ->  ps ) )
52, 4impbid 120 1  |-  ( ph  ->  ( ps  <->  ch )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 100  ax-ia3 101  ax-in2 545
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  pm5.21ni  619  bianfd  855  abvor0dc  3242  nn0eln0  4341  nntri3  6075  fin0  6342  xrlttri3  8718  nltpnft  8730  ngtmnft  8731  xrrebnd  8732
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