Theorem pm2.24 622

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		pm2.21 618	. 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 616

This theorem is referenced by:  pm2.24d  623  pm2.53  724  pm2.82  814  pm4.81dc  910  dedlema  972  alexim  1669  eqneqall  2388  elnelall  2485  sotritric  4389  ltxrlt  8173  zltnle  9453  elfzonlteqm1  10376  qltnle  10423  hashfzp1  11006  swrdccat3blem  11230  dfgcd2  12450  oddprmdvds  12792  2lgsoddprm  15705  bj-fast  15877  nnnotnotr  16125