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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  2314  pssnn  8138  alephadd  9359  axextnd  9373  axunnd  9378  axpownd  9383  axregndlem2  9385  axregnd  9386  axinfndlem1  9387  axinfnd  9388  2cshwcshw  13524  ressress  15878  frgrreg  27140  bj-hbaeb2  32501  hbae-o  33707  hbequid  33713  ax5eq  33736  ax5el  33741
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