Theorem pm2.53 722

Description: Theorem *2.53 of [WhiteheadRussell] p. 107. This holds intuitionistically, although its converse does not (see pm2.54dc 891). (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		pm2.24 621	. 2 |- ( ph -> ( -. ph -> ps ) )
2		ax-1 6	. 2 |- ( ps -> ( -. ph -> ps ) )
3	1, 2	jaoi 716	1 |- ( ( ph \/ ps ) -> ( -. ph -> ps ) )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 708

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in2 615  ax-io 709

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  ori  723  ord  724  orel1  725  pm2.63  800  notnotrdc  843  dfordc  892  pm5.6r  927  xorbin  1384  19.33b2  1629  r19.30dc  2624  onsucelsucexmid  4531  oprabidlem  5908  omnimkv  7156  xnn0nnn0pnf  9254  absle  11100