Theorem or32 719

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 716	. 2 |- ( ( ( ph \/ ps ) \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )
2		or12 715	. 2 |- ( ( ph \/ ( ps \/ ch ) ) <-> ( ps \/ ( ph \/ ch ) ) )
3		orcom 679	. 2 |- ( ( ps \/ ( ph \/ ch ) ) <-> ( ( ph \/ ch ) \/ ps ) )
4	1, 2, 3	3bitri 204	1 |- ( ( ( ph \/ ps ) \/ ch ) <-> ( ( ph \/ ch ) \/ ps ) )

Syntax hints:   <-> wb 103   \/ wo 661

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  xrnepnf  8854