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Theorem 2falsed 617
Description: Two falsehoods are equivalent (deduction rule). (Contributed by NM, 11-Oct-2013.)
Hypotheses
Ref Expression
2falsed.1 (φ → ¬ ψ)
2falsed.2 (φ → ¬ χ)
Assertion
Ref Expression
2falsed (φ → (ψχ))

Proof of Theorem 2falsed
StepHypRef Expression
1 2falsed.1 . . 3 (φ → ¬ ψ)
21pm2.21d 549 . 2 (φ → (ψχ))
3 2falsed.2 . . 3 (φ → ¬ χ)
43pm2.21d 549 . 2 (φ → (χψ))
52, 4impbid 120 1 (φ → (ψχ))
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  618  bianfd  854  abvor0dc  3236  nn0eln0  4284  nntri3  6014  xrlttri3  8468  nltpnft  8480  ngtmnft  8481  xrrebnd  8482
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