Theorem pm2.24 624

Description: Theorem *2.24 of [WhiteheadRussell] p. 104. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm2.24	|- ( ph -> ( -. ph -> ps ) )

Proof of Theorem pm2.24

Step	Hyp	Ref	Expression
1		pm2.21 620	. 2 |- ( -. ph -> ( ph -> ps ) )
2	1	com12 30	1 |- ( ph -> ( -. ph -> ps ) )

Syntax hints:   -. wn 3   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in2 618

This theorem is referenced by:  pm2.24d  625  pm2.53  727  pm2.82  817  pm4.81dc  913  dedlema  975  ifp2  986  alexim  1691  eqneqall  2410  elnelall  2507  sotritric  4414  ltxrlt  8208  zltnle  9488  elfzonlteqm1  10411  qltnle  10458  hashfzp1  11041  swrdccat3blem  11266  dfgcd2  12530  oddprmdvds  12872  2lgsoddprm  15786  bj-fast  16063  nnnotnotr  16311