Theorem pm2.21ddALT 122

Description: Alternate proof of pm2.21dd 194. (Contributed by Mario Carneiro, 9-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
pm2.21ddALT.1	⊢ (𝜑 → 𝜓)
pm2.21ddALT.2	⊢ (𝜑 → ¬ 𝜓)

Assertion

Ref	Expression
pm2.21ddALT	⊢ (𝜑 → 𝜒)

Proof of Theorem pm2.21ddALT

Step	Hyp	Ref	Expression
1		pm2.21ddALT.1	. 2 ⊢ (𝜑 → 𝜓)
2		pm2.21ddALT.2	. . 3 ⊢ (𝜑 → ¬ 𝜓)
3	2	pm2.21d 121	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
4	1, 3	mpd 15	1 ⊢ (𝜑 → 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: (None)