Theorem orel2 716

Description: Elimination of disjunction by denial of a disjunct. Theorem *2.56 of [WhiteheadRussell] p. 107. (Contributed by NM, 12-Aug-1994.) (Proof shortened by Wolf Lammen, 5-Apr-2013.)

Assertion

Ref	Expression
orel2	|- ( -. ph -> ( ( ps \/ ph ) -> ps ) )

Proof of Theorem orel2

Step	Hyp	Ref	Expression
1		idd 21	. 2 |- ( -. ph -> ( ps -> ps ) )
2		pm2.21 607	. 2 |- ( -. ph -> ( ph -> ps ) )
3	1, 2	jaod 707	1 |- ( -. ph -> ( ( ps \/ ph ) -> ps ) )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 698

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 605  ax-io 699

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  biorfi  736  pm2.64  791  stdcn  837  pm5.71dc  951  ecased  1339  19.30dc  1615  dveeq2  1803  prel12  3751  funun  5232