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  723  pm2.82  813  pm4.81dc  909  dedlema  971  alexim  1659  eqneqall  2377  elnelall  2474  sotritric  4359  ltxrlt  8092  zltnle  9372  elfzonlteqm1  10286  qltnle  10333  hashfzp1  10916  dfgcd2  12181  oddprmdvds  12523  2lgsoddprm  15354  bj-fast  15387  nnnotnotr  15636