Theorem pm2.52 147

Description: Theorem *2.52 of [WhiteheadRussell] p. 107. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 8-Oct-2012.)

Assertion

Ref	Expression
pm2.52	⊢ (¬ (φ → ψ) → (¬ φ → ¬ ψ))

Proof of Theorem pm2.52

Step	Hyp	Ref	Expression
1		pm2.521 146	. 2 ⊢ (¬ (φ → ψ) → (ψ → φ))
2	1	con3d 125	1 ⊢ (¬ (φ → ψ) → (¬ φ → ¬ ψ))

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)