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Theorem pm2.61iii 178
 Description: Inference eliminating three antecedents. (Contributed by NM, 2-Jan-2002.) (Proof shortened by Wolf Lammen, 22-Sep-2013.)
Hypotheses
Ref Expression
pm2.61iii.1 𝜑 → (¬ 𝜓 → (¬ 𝜒𝜃)))
pm2.61iii.2 (𝜑𝜃)
pm2.61iii.3 (𝜓𝜃)
pm2.61iii.4 (𝜒𝜃)
Assertion
Ref Expression
pm2.61iii 𝜃

Proof of Theorem pm2.61iii
StepHypRef Expression
1 pm2.61iii.4 . 2 (𝜒𝜃)
2 pm2.61iii.1 . . 3 𝜑 → (¬ 𝜓 → (¬ 𝜒𝜃)))
3 pm2.61iii.2 . . . 4 (𝜑𝜃)
43a1d 25 . . 3 (𝜑 → (¬ 𝜒𝜃))
5 pm2.61iii.3 . . . 4 (𝜓𝜃)
65a1d 25 . . 3 (𝜓 → (¬ 𝜒𝜃))
72, 4, 6pm2.61ii 176 . 2 𝜒𝜃)
81, 7pm2.61i 175 1 𝜃
 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:  axrepnd  9295  axacndlem4  9311  axacndlem5  9312  axacnd  9313
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