Theorem con2 82

Description: Contraposition. Theorem *2.03 of [WhiteheadRussell] p. 100.

Assertion

Ref	Expression
con2	⊢ ((φ → ¬ ψ) → (ψ → ¬ φ))

Proof of Theorem con2

Step	Hyp	Ref	Expression
1		nega 78	. . 3 ⊢ (¬ ¬ φ → φ)
2	1	syl4 19	. 2 ⊢ ((φ → ¬ ψ) → (¬ ¬ φ → ¬ ψ))
3	2	a3d 70	1 ⊢ ((φ → ¬ ψ) → (ψ → ¬ φ))

Syntax hints:  ¬ wn 1   → wi 2

This theorem is referenced by:  con2d 83  bi2.03 144  pm5.18 497  mt2bi 535  rankr1 3518

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

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