Theorem pm2.61 183

Description: Theorem *2.61 of [WhiteheadRussell] p. 107. Useful for eliminating an antecedent. (Contributed by NM, 4-Jan-1993.) (Proof shortened by Wolf Lammen, 22-Sep-2013.)

Assertion

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

Proof of Theorem pm2.61

Step	Hyp	Ref	Expression
1		pm2.6 182	. 2 |- ( ( -. ph -> ps ) -> ( ( ph -> ps ) -> ps ) )
2	1	com12 32	1 |- ( ( ph -> ps ) -> ( ( -. ph -> ps ) -> 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:  bnj1109  30857  jath  31609  isltrn2N  35406  ltrnid  35421  ltrneq  35435  onfrALT  38764  onfrALTVD  39127