Theorem orel1 679

Description: Elimination of disjunction by denial of a disjunct. Theorem *2.55 of [WhiteheadRussell] p. 107. (Contributed by NM, 12-Aug-1994.) (Proof shortened by Wolf Lammen, 21-Jul-2012.)

Assertion

Ref	Expression
orel1	|- ( -. ph -> ( ( ph \/ ps ) -> ps ) )

Proof of Theorem orel1

Step	Hyp	Ref	Expression
1		pm2.53 676	. 2 |- ( ( ph \/ ps ) -> ( -. ph -> ps ) )
2	1	com12 30	1 |- ( -. ph -> ( ( ph \/ ps ) -> ps ) )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 664

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 580  ax-io 665

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  biorf  698  pm2.25dc  830  pm2.85dc  849  euor2  2006  prel12  3615  funun  5058  acexmidlema  5643  acexmidlemb  5644