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Theorem pm2.61ii 177
 Description: Inference eliminating two antecedents. (Contributed by NM, 4-Jan-1993.) (Proof shortened by Josh Purinton, 29-Dec-2000.)
Hypotheses
Ref Expression
pm2.61ii.1 𝜑 → (¬ 𝜓𝜒))
pm2.61ii.2 (𝜑𝜒)
pm2.61ii.3 (𝜓𝜒)
Assertion
Ref Expression
pm2.61ii 𝜒

Proof of Theorem pm2.61ii
StepHypRef Expression
1 pm2.61ii.2 . 2 (𝜑𝜒)
2 pm2.61ii.1 . . 3 𝜑 → (¬ 𝜓𝜒))
3 pm2.61ii.3 . . 3 (𝜓𝜒)
42, 3pm2.61d2 172 . 2 𝜑𝜒)
51, 4pm2.61i 176 1 𝜒
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8 This theorem is referenced by:  pm2.61iii  179  hbae  2457  pssnn  8343  alephadd  9591  axextnd  9605  axunnd  9610  axpownd  9615  axregndlem2  9617  axregnd  9618  axinfndlem1  9619  axinfnd  9620  2cshwcshw  13771  ressress  16140  frgrreg  27562  bj-hbaeb2  33111  hbae-o  34692  hbequid  34698  ax5eq  34721  ax5el  34726  odd2prm2  42137
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