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 → (¬ 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 172	. 2 ⊢ (¬ 𝜑 → 𝜒)
5	1, 4	pm2.61i 176	1 ⊢ 𝜒

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  2315  pssnn  8178  alephadd  9399  axextnd  9413  axunnd  9418  axpownd  9423  axregndlem2  9425  axregnd  9426  axinfndlem1  9427  axinfnd  9428  2cshwcshw  13571  ressress  15938  frgrreg  27252  bj-hbaeb2  32805  hbae-o  34188  hbequid  34194  ax5eq  34217  ax5el  34222  odd2prm2  41627