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Theorem 2falsed 651
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 582 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
3 2falsed.2 . . 3  |-  ( ph  ->  -.  ch )
43pm2.21d 582 . 2  |-  ( ph  ->  ( ch  ->  ps ) )
52, 4impbid 127 1  |-  ( ph  ->  ( ps  <->  ch )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 105  ax-ia3 106  ax-in2 578
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  pm5.21ni  652  bianfd  890  abvor0dc  3285  nn0eln0  4387  nntri3  6161  fin0  6441  xrlttri3  9000  nltpnft  9012  ngtmnft  9013  xrrebnd  9014  hashnncl  9872  mod2eq1n2dvds  10486  m1exp1  10508
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