Theorem pm2.24 616

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		pm2.21 612	. 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 610

This theorem is referenced by:  pm2.24d  617  pm2.53  717  pm2.82  807  pm4.81dc  903  dedlema  964  alexim  1638  eqneqall  2350  elnelall  2447  sotritric  4307  ltxrlt  7972  zltnle  9245  elfzonlteqm1  10153  qltnle  10189  hashfzp1  10746  dfgcd2  11956  oddprmdvds  12293  bj-fast  13735  nnnotnotr  13985