Theorem or32 513

Description: A rearrangement of disjuncts. (Contributed by NM, 18-Oct-1995.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)

Assertion

Ref	Expression
or32	|- (((ph \/ ps) \/ ch) <-> ((ph \/ ch) \/ ps))

Proof of Theorem or32

Step	Hyp	Ref	Expression
1		orass 510	. 2 |- (((ph \/ ps) \/ ch) <-> (ph \/ (ps \/ ch)))
2		or12 509	. 2 |- ((ph \/ (ps \/ ch)) <-> (ps \/ (ph \/ ch)))
3		orcom 376	. 2 |- ((ps \/ (ph \/ ch)) <-> ((ph \/ ch) \/ ps))
4	1, 2, 3	3bitri 262	1 |- (((ph \/ ps) \/ ch) <-> ((ph \/ ch) \/ ps))

Syntax hints:   <-> wb 176   \/ wo 357

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

This theorem is referenced by:  sspsstri  3372  sfin111  4537