Theorem pm2.53 641

Description: Theorem *2.53 of [WhiteheadRussell] p. 107. This holds intuitionistically, although its converse does not (see pm2.54dc 790). (Contributed by NM, 3-Jan-2005.) (Revised by NM, 31-Jan-2015.)

Assertion

Ref	Expression
pm2.53	|- ( ( ph \/ ps ) -> ( -. ph -> ps ) )

Proof of Theorem pm2.53

Step	Hyp	Ref	Expression
1		pm2.24 551	. 2 |- ( ph -> ( -. ph -> ps ) )
2		ax-1 5	. 2 |- ( ps -> ( -. ph -> ps ) )
3	1, 2	jaoi 636	1 |- ( ( ph \/ ps ) -> ( -. ph -> ps ) )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 629

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in2 545  ax-io 630

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  ori  642  ord  643  orel1  644  pm2.63  713  notnotrdc  751  dfordc  791  pm5.6r  836  xorbin  1275  19.33b2  1520  onsucelsucexmid  4255  oprabidlem  5536  absle  9685