Theorem con3ALT2 41823

Description: Contraposition. Alternate proof of con3 156. This proof is con3ALTVD 42209 automatically translated and minimized. (Contributed by Alan Sare, 21-Apr-2013.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
con3ALT2	⊢ ((𝜑 → 𝜓) → (¬ 𝜓 → ¬ 𝜑))

Proof of Theorem con3ALT2

Step	Hyp	Ref	Expression
1		notnotr 132	. . 3 ⊢ (¬ ¬ 𝜑 → 𝜑)
2	1	imim1i 63	. 2 ⊢ ((𝜑 → 𝜓) → (¬ ¬ 𝜑 → 𝜓))
3	2	con1d 147	1 ⊢ ((𝜑 → 𝜓) → (¬ 𝜓 → ¬ 𝜑))

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)