Theorem pm2.65 115

Description: Theorem *2.65 of [WhiteheadRussell] p. 107. Useful for eliminating a consequent.

Assertion

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

Proof of Theorem pm2.65

Step	Hyp	Ref	Expression
1		pm3.2im 107	. . 3 ⊢ (φ → (ψ → ¬ (φ → ¬ ψ)))
2	1	a2i 8	. 2 ⊢ ((φ → ψ) → (φ → ¬ (φ → ¬ ψ)))
3	2	con2d 83	1 ⊢ ((φ → ψ) → ((φ → ¬ ψ) → ¬ φ))

Syntax hints:  ¬ wn 1   → wi 2

This theorem is referenced by:  pm2.65d 117  pm5.18 497

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

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