Theorem orabs 583

Description: Absorption of redundant internal disjunct. Compare Theorem *4.45 of [WhiteheadRussell] p. 119.

Assertion

Ref	Expression
orabs	|- (ph <-> ((ph \/ ps) /\ ph))

Proof of Theorem orabs

Step	Hyp	Ref	Expression
1		orc 269	. . 3 |- (ph -> (ph \/ ps))
2	1	ancri 297	. 2 |- (ph -> ((ph \/ ps) /\ ph))
3		pm3.27 323	. 2 |- (((ph \/ ps) /\ ph) -> ph)
4	2, 3	impbi 157	1 |- (ph <-> ((ph \/ ps) /\ ph))

Syntax hints:   <-> wb 146   \/ wo 222   /\ wa 223

This theorem is referenced by:  prlem2 773

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  df-an 225

Copyright terms: Public domain