Theorem pm2.5 164

Description: Theorem *2.5 of [WhiteheadRussell] p. 107. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 9-Oct-2012.)

Assertion

Ref	Expression
pm2.5	|- ( -. ( ph -> ps ) -> ( -. ph -> ps ) )

Proof of Theorem pm2.5

Step	Hyp	Ref	Expression
1		simplim 163	. 2 |- ( -. ( ph -> ps ) -> ph )
2	1	pm2.24d 147	1 |- ( -. ( ph -> ps ) -> ( -. ph -> ps ) )

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:  pm5.11  928