Theorem orel2 252

Description: Elimination of disjunction by denial of a disjunct. Theorem *2.56 of [WhiteheadRussell] p. 107.

Assertion

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

Proof of Theorem orel2

Step	Hyp	Ref	Expression
1		orel1 251	. 2 |- (-. ph -> ((ph \/ ps) -> ps))
2		orcom 246	. 2 |- ((ps \/ ph) <-> (ph \/ ps))
3	1, 2	syl5ib 206	1 |- (-. ph -> ((ps \/ ph) -> ps))

Syntax hints:  -. wn 2   -> wi 3   \/ wo 222

This theorem is referenced by:  pm2.64 429  pm5.61 447  pm2.74 573  pm5.71 748  prel12 2484  funun 3554

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-or 224

Copyright terms: Public domain