Theorem orel1 643

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		pm2.53 640	. 2 |- ((ph \/ ps) -> (-. ph -> ps))
2	1	com12 27	1 |- (-. ph -> ((ph \/ ps) -> ps))

Syntax hints:  -. wn 3   -> wi 4   \/ wo 628

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in2 545  ax-io 629

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  biorf  662  pm2.25dc  791  pm2.85dc  810  euor2  1955  prel12  3533  funun  4887  acexmidlema  5446  acexmidlemb  5447