Theorem pm2.521 166

Description: Theorem *2.521 of [WhiteheadRussell] p. 107. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 8-Oct-2012.)

Assertion

Ref	Expression
pm2.521	|- ( -. ( ph -> ps ) -> ( ps -> ph ) )

Proof of Theorem pm2.521

Step	Hyp	Ref	Expression
1		simplim 163	. 2 |- ( -. ( ph -> ps ) -> ph )
2	1	a1d 25	1 |- ( -. ( ph -> ps ) -> ( ps -> ph ) )

Syntax hints:   -. wn 3   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by:  pm2.52  167  ifpimim  37854