Theorem pm2.24 630

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		pm2.21 626	. 2 |- ( -. ph -> ( ph -> ps ) )
2	1	com12 30	1 |- ( ph -> ( -. ph -> ps ) )

This proof depends on syntax axioms:   -. wn 3   -> wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in2 624

This theorem is used by:  pm2.24d  631  pm2.53  734  pm2.82  824  pm4.81dc  920  dedlema  982  ifp2  993  alexim  1698  eqneqall  2430  elnelall  2527  sotritric  4471  ltxrlt  8397  zltnle  9701  elfzonlteqm1  10645  qltnle  10695  hashfzp1  11287  swrdccat3blem  11533  dfgcd2  12816  oddprmdvds  13162  2lgsoddprm  16437  bj-fast  16974  nnnotnotr  17221