Theorem pm2.65 164

Description: Theorem *2.65 of [WhiteheadRussell] p. 107. Proof by contradiction. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 8-Mar-2013.)

Assertion

Ref	Expression
pm2.65	⊢ ((φ → ψ) → ((φ → ¬ ψ) → ¬ φ))

Proof of Theorem pm2.65

Step	Hyp	Ref	Expression
1		idd 21	. 2 ⊢ ((φ → ψ) → (¬ φ → ¬ φ))
2		con3 126	. 2 ⊢ ((φ → ψ) → (¬ ψ → ¬ φ))
3	1, 2	jad 154	1 ⊢ ((φ → ψ) → ((φ → ¬ ψ) → ¬ φ))

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:  pm4.82  894