Theorem orel1 732

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		pm2.53 729	. 2 |- ( ( ph \/ ps ) -> ( -. ph -> ps ) )
2	1	com12 30	1 |- ( -. ph -> ( ( ph \/ ps ) -> ps ) )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 715

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 620  ax-io 716

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  biorf  751  pm2.25dc  900  pm2.85dc  912  euor2  2138  prel12  3854  funun  5371  acexmidlema  6008  acexmidlemb  6009  sup3exmid  9136  pythagtriplem4  12840  umgrislfupgrenlem  15980