Theorem pm2.24 586

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		pm2.21 582	. 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-1 5  ax-2 6  ax-mp 7  ax-in2 580

This theorem is referenced by:  pm2.24d  587  pm2.53  676  pm2.82  761  pm4.81dc  852  dedlema  915  alexim  1581  eqneqall  2265  sotritric  4142  ltxrlt  7531  zltnle  8766  elfzonlteqm1  9586  qltnle  9622  hashfzp1  10197  dfgcd2  11096