Theorem pm2.61 109

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

Assertion

Ref	Expression
pm2.61	|- ((ph -> ps) -> ((-. ph -> ps) -> ps))

Proof of Theorem pm2.61

Step	Hyp	Ref	Expression
1		syl1 16	. . 3 |- ((ph -> ps) -> ((-. ps -> ph) -> (-. ps -> ps)))
2		pm2.18 75	. . 3 |- ((-. ps -> ps) -> ps)
3	1, 2	syl6 23	. 2 |- ((ph -> ps) -> ((-. ps -> ph) -> ps))
4		con1 84	. 2 |- ((-. ph -> ps) -> (-. ps -> ph))
5	3, 4	syl5 22	1 |- ((ph -> ps) -> ((-. ph -> ps) -> ps))

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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