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Theorem pm2.61ii 176
 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 171 . 2 𝜑𝜒)
51, 4pm2.61i 175 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  178  hbae  2303  pssnn  8063  alephadd  9278  axextnd  9292  axunnd  9297  axpownd  9302  axregndlem2  9304  axregnd  9305  axinfndlem1  9306  axinfnd  9307  2cshwcshw  13422  ressress  15765  frgrareg  26644  bj-hbaeb2  31993  hbae-o  33206  hbequid  33212  ax5eq  33235  ax5el  33240  av-frgrareg  41548
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