Theorem oranabs 829

Description: Absorb a disjunct into a conjunct. (Contributed by Roy F. Longton, 23-Jun-2005.) (Proof shortened by Wolf Lammen, 10-Nov-2013.)

Assertion

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

Proof of Theorem oranabs

Step	Hyp	Ref	Expression
1		biortn 395	. . 3 |- (ps -> (ph <-> (-. ps \/ ph)))
2		orcom 376	. . 3 |- ((-. ps \/ ph) <-> (ph \/ -. ps))
3	1, 2	syl6rbb 253	. 2 |- (ps -> ((ph \/ -. ps) <-> ph))
4	3	pm5.32ri 619	1 |- (((ph \/ -. ps) /\ ps) <-> (ph /\ ps))

Syntax hints:  -. wn 3   <-> wb 176   \/ wo 357   /\ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360

This theorem is referenced by: (None)