Theorem orel1 251

Description: Elimination of disjunction by denial of a disjunct. Theorem *2.55 of [WhiteheadRussell] p. 107.

Assertion

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

Proof of Theorem orel1

Step	Hyp	Ref	Expression
1		df-or 224	. . 3 |- ((ph \/ ps) <-> (-. ph -> ps))
2	1	biimp 151	. 2 |- ((ph \/ ps) -> (-. ph -> ps))
3	2	com12 11	1 |- (-. ph -> ((ph \/ ps) -> ps))

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

This theorem is referenced by:  orel2 252  pm2.25 253  pm2.53 254  prel12 2475  funun 3540  tfrlem13 3908

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