Theorem pm2.86 63

Description: Converse of axiom ax-2 4. Theorem *2.86 of [WhiteheadRussell] p. 108.

Assertion

Ref	Expression
pm2.86	⊢ (((φ → ψ) → (φ → χ)) → (φ → (ψ → χ)))

Proof of Theorem pm2.86

Step	Hyp	Ref	Expression
1		ax-1 3	. . 3 ⊢ (ψ → (φ → ψ))
2	1	syl4 19	. 2 ⊢ (((φ → ψ) → (φ → χ)) → (ψ → (φ → χ)))
3	2	com23 32	1 ⊢ (((φ → ψ) → (φ → χ)) → (φ → (ψ → χ)))

Syntax hints:   → wi 2

This theorem is referenced by:  pm2.86i 64  pm2.86d 65  imdi 147

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

metamath.org