Theorem pm2.61 124

Description: Theorem *2.61 of [WhiteheadRussell] p. 107. Useful for eliminating an antecedent. (The proof was shortened by O'Cat, 19-Feb-2008.)

Assertion

Ref	Expression
pm2.61	⊢ ((φ → ψ) → ((¬ φ → ψ) → ψ))

Proof of Theorem pm2.61

Step	Hyp	Ref	Expression
1		con1 92	. . 3 ⊢ ((¬ φ → ψ) → (¬ ψ → φ))
2	1	imim1d 28	. 2 ⊢ ((¬ φ → ψ) → ((φ → ψ) → (¬ ψ → ψ)))
3		pm2.18 81	. 2 ⊢ ((¬ ψ → ψ) → ψ)
4	2, 3	syl6com 53	1 ⊢ ((φ → ψ) → ((¬ φ → ψ) → ψ))

Syntax hints:  ¬ wn 2   → wi 3

This theorem is referenced by:  pm2.61i 126  pm2.6 133  pm5.18 659  undif4 2321

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

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