Theorem con34b 283

Description: Contraposition. Theorem *4.1 of [WhiteheadRussell] p. 116. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
con34b	⊢ ((φ → ψ) ↔ (¬ ψ → ¬ φ))

Proof of Theorem con34b

Step	Hyp	Ref	Expression
1		con3 126	. 2 ⊢ ((φ → ψ) → (¬ ψ → ¬ φ))
2		ax-3 8	. 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:  mtt  329  pm4.14  561  sscon34  3662  evenodddisjlem1  4516