Theorem con5i 42143

Description: Inference form of con5 42142. (Contributed by Alan Sare, 21-Apr-2013.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
con5i.1	⊢ (𝜑 ↔ ¬ 𝜓)

Assertion

Ref	Expression
con5i	⊢ (¬ 𝜑 → 𝜓)

Proof of Theorem con5i

Step	Hyp	Ref	Expression
1		con5i.1	. 2 ⊢ (𝜑 ↔ ¬ 𝜓)
2		con5 42142	. 2 ⊢ ((𝜑 ↔ ¬ 𝜓) → (¬ 𝜑 → 𝜓))
3	1, 2	ax-mp 5	1 ⊢ (¬ 𝜑 → 𝜓)

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 205

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206

This theorem is referenced by:  vk15.4j  42148  vk15.4jVD  42534