Theorem con5 42031

Description: Biconditional contraposition variation. This proof is con5VD 42409 automatically translated and minimized. (Contributed by Alan Sare, 21-Apr-2013.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
con5	⊢ ((𝜑 ↔ ¬ 𝜓) → (¬ 𝜑 → 𝜓))

Proof of Theorem con5

Step	Hyp	Ref	Expression
1		biimpr 219	. 2 ⊢ ((𝜑 ↔ ¬ 𝜓) → (¬ 𝜓 → 𝜑))
2	1	con1d 145	1 ⊢ ((𝜑 ↔ ¬ 𝜓) → (¬ 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:  con5i  42032