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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 (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 582 . 2 (𝜑 → (𝜓𝜒))
3 2falsed.2 . . 3 (𝜑 → ¬ 𝜒)
43pm2.21d 582 . 2 (𝜑 → (𝜒𝜓))
52, 4impbid 127 1 (𝜑 → (𝜓𝜒))
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  3276  nn0eln0  4367  nntri3  6141  fin0  6419  xrlttri3  8948  nltpnft  8960  ngtmnft  8961  xrrebnd  8962  sizenncl  9820  mod2eq1n2dvds  10423  m1exp1  10445
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