Theorem pm2.53 673

Description: Theorem *2.53 of [WhiteheadRussell] p. 107. This holds intuitionistically, although its converse does not (see pm2.54dc 823). (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		pm2.24 583	. 2 |- ( ph -> ( -. ph -> ps ) )
2		ax-1 5	. 2 |- ( ps -> ( -. ph -> ps ) )
3	1, 2	jaoi 668	1 |- ( ( ph \/ ps ) -> ( -. ph -> ps ) )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 661

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in2 577  ax-io 662

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  ori  674  ord  675  orel1  676  pm2.63  746  notnotrdc  784  dfordc  824  pm5.6r  869  xorbin  1315  19.33b2  1560  onsucelsucexmid  4273  oprabidlem  5556  absle  9975