Theorem oranabs 582

Description: Absorb a disjunct into a conjunct. (Contributed by Roy F. Longton 23-Jun-2005.)

Assertion

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

Proof of Theorem oranabs

Step	Hyp	Ref	Expression
1		pm5.61 447	. 2 |- (((ph \/ -. ps) /\ -. -. ps) <-> (ph /\ -. -. ps))
2		pm4.13 161	. . 3 |- (ps <-> -. -. ps)
3	2	anbi2i 480	. 2 |- (((ph \/ -. ps) /\ ps) <-> ((ph \/ -. ps) /\ -. -. ps))
4	2	anbi2i 480	. 2 |- ((ph /\ ps) <-> (ph /\ -. -. ps))
5	1, 3, 4	3bitr4 183	1 |- (((ph \/ -. ps) /\ ps) <-> (ph /\ ps))

Syntax hints:  -. wn 2   <-> wb 146   \/ wo 222   /\ wa 223

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

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