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	|- ((ph -> ps) -> ((-. ph -> ps) -> ps))

Proof of Theorem pm2.61

Step	Hyp	Ref	Expression
1		con1 92	. . 3 |- ((-. ph -> ps) -> (-. ps -> ph))
2	1	imim1d 28	. 2 |- ((-. ph -> ps) -> ((ph -> ps) -> (-. ps -> ps)))
3		pm2.18 81	. 2 |- ((-. ps -> ps) -> ps)
4	2, 3	syl6com 53	1 |- ((ph -> ps) -> ((-. ph -> ps) -> ps))

Syntax hints:  -. wn 2   -> wi 3

This theorem is referenced by:  pm2.61i 126  pm2.6 133  pm5.18 657  undif4 2296

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

Copyright terms: Public domain