Theorem or32 759

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 756	. 2 |- ( ( ( ph \/ ps ) \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )
2		or12 755	. 2 |- ( ( ph \/ ( ps \/ ch ) ) <-> ( ps \/ ( ph \/ ch ) ) )
3		orcom 717	. 2 |- ( ( ps \/ ( ph \/ ch ) ) <-> ( ( ph \/ ch ) \/ ps ) )
4	1, 2, 3	3bitri 205	1 |- ( ( ( ph \/ ps ) \/ ch ) <-> ( ( ph \/ ch ) \/ ps ) )

Syntax hints:   <-> wb 104   \/ wo 697

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  xrnepnf  9558