Theorem con1b 323

Description: Contraposition. Bidirectional version of con1 120. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
con1b	⊢ ((¬ φ → ψ) ↔ (¬ ψ → φ))

Proof of Theorem con1b

Step	Hyp	Ref	Expression
1		con1 120	. 2 ⊢ ((¬ φ → ψ) → (¬ ψ → φ))
2		con1 120	. 2 ⊢ ((¬ ψ → φ) → (¬ φ → ψ))
3	1, 2	impbii 180	1 ⊢ ((¬ φ → ψ) ↔ (¬ ψ → φ))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 176

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 177

This theorem is referenced by: (None)