Theorem pm2.61ii 185

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 → (¬ 𝜓 → 𝜒))
pm2.61ii.2	⊢ (𝜑 → 𝜒)
pm2.61ii.3	⊢ (𝜓 → 𝜒)

Assertion

Ref	Expression
pm2.61ii	⊢ 𝜒

Proof of Theorem pm2.61ii

Step	Hyp	Ref	Expression
1		pm2.61ii.2	. 2 ⊢ (𝜑 → 𝜒)
2		pm2.61ii.1	. . 3 ⊢ (¬ 𝜑 → (¬ 𝜓 → 𝜒))
3		pm2.61ii.3	. . 3 ⊢ (𝜓 → 𝜒)
4	2, 3	pm2.61d2 183	. 2 ⊢ (¬ 𝜑 → 𝜒)
5	1, 4	pm2.61i 184	1 ⊢ 𝜒

This proof depends on syntax axioms:  ¬ wn 3   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is used by:  pm2.61iii  187  hbae  2465  pssnn  9160  alephadd  10577  axextnd  10591  axunnd  10596  axpownd  10601  axregndlem2  10603  axregnd  10604  axinfndlem1  10605  axinfnd  10606  2cshwcshw  14886  ressress  17329  frgrreg  30816  bj-hbaeb2  37510  hbae-o  39735  hbequid  39741  ax5eq  39764  ax5el  39769  odd2prm2  48541