Theorem con1 84

Description: Contraposition. Theorem *2.15 of [WhiteheadRussell] p. 102.

Assertion

Ref	Expression
con1	⊢ ((¬ φ → ψ) → (¬ ψ → φ))

Proof of Theorem con1

Step	Hyp	Ref	Expression
1		negb 79	. . 3 ⊢ (ψ → ¬ ¬ ψ)
2	1	syl3 18	. 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:  con1d 85  pm2.36 91  pm2.61 109  bi2.15 145  jao 274  eqs2 829  uzwo 4605  nnwoOLD 4608  elspansn5t 5479

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

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