Theorem pm2.53 717

Description: Theorem *2.53 of [WhiteheadRussell] p. 107. This holds intuitionistically, although its converse does not (see pm2.54dc 886). (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		pm2.24 616	. 2 |- ( ph -> ( -. ph -> ps ) )
2		ax-1 6	. 2 |- ( ps -> ( -. ph -> ps ) )
3	1, 2	jaoi 711	1 |- ( ( ph \/ ps ) -> ( -. ph -> ps ) )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 703

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in2 610  ax-io 704

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  ori  718  ord  719  orel1  720  pm2.63  795  notnotrdc  838  dfordc  887  pm5.6r  922  xorbin  1379  19.33b2  1622  r19.30dc  2617  onsucelsucexmid  4514  oprabidlem  5884  omnimkv  7132  xnn0nnn0pnf  9211  absle  11053