Theorem pm2.86 69

Description: Converse of axiom ax-2 5. Theorem *2.86 of [WhiteheadRussell] p. 108.

Assertion

Ref	Expression
pm2.86	|- (((ph -> ps) -> (ph -> ch)) -> (ph -> (ps -> ch)))

Proof of Theorem pm2.86

Step	Hyp	Ref	Expression
1		ax-1 4	. . 3 |- (ps -> (ph -> ps))
2	1	imim1i 16	. 2 |- (((ph -> ps) -> (ph -> ch)) -> (ps -> (ph -> ch)))
3	2	com23 32	1 |- (((ph -> ps) -> (ph -> ch)) -> (ph -> (ps -> ch)))

Syntax hints:   -> wi 3

This theorem is referenced by:  pm2.86i 70  pm2.86d 71  imdi 168  pm5.41 169

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

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