Theorem pm2.61 109

Description: Theorem *2.61 of [WhiteheadRussell] p. 107. Useful for eliminating an antecedent.

Assertion

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

Proof of Theorem pm2.61

Step	Hyp	Ref	Expression
1		syl1 16	. . 3 ⊢ ((φ → ψ) → ((¬ ψ → φ) → (¬ ψ → ψ)))
2		pm2.18 75	. . 3 ⊢ ((¬ ψ → ψ) → ψ)
3	1, 2	syl6 23	. 2 ⊢ ((φ → ψ) → ((¬ ψ → φ) → ψ))
4		con1 84	. 2 ⊢ ((¬ φ → ψ) → (¬ ψ → φ))
5	3, 4	syl5 22	1 ⊢ ((φ → ψ) → ((¬ φ → ψ) → ψ))

Syntax hints:  ¬ wn 1   → wi 2

This theorem is referenced by:  pm2.61i 110  dfor2 199  pm5.18 497  undif4 1744

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

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