Theorem or12 509

Description: Swap two disjuncts. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 14-Nov-2012.)

Assertion

Ref	Expression
or12	|- ((ph \/ (ps \/ ch)) <-> (ps \/ (ph \/ ch)))

Proof of Theorem or12

Step	Hyp	Ref	Expression
1		pm1.5 508	. 2 |- ((ph \/ (ps \/ ch)) -> (ps \/ (ph \/ ch)))
2		pm1.5 508	. 2 |- ((ps \/ (ph \/ ch)) -> (ph \/ (ps \/ ch)))
3	1, 2	impbii 180	1 |- ((ph \/ (ps \/ ch)) <-> (ps \/ (ph \/ ch)))

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:  orass  510  or32  513  or4  514  3orcoma  942