Theorem oranabs 765

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 700	. . 3 |- ( ps -> ( ph <-> ( -. ps \/ ph ) ) )
2		orcom 683	. . 3 |- ( ( -. ps \/ ph ) <-> ( ph \/ -. ps ) )
3	1, 2	syl6rbb 196	. 2 |- ( ps -> ( ( ph \/ -. ps ) <-> ph ) )
4	3	pm5.32ri 444	1 |- ( ( ( ph \/ -. ps ) /\ ps ) <-> ( ph /\ ps ) )

Syntax hints:   -. wn 3   /\ wa 103   <-> wb 104   \/ wo 665

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 580  ax-in2 581  ax-io 666

This theorem depends on definitions:  df-bi 116

This theorem is referenced by: (None)