Theorem or42 515

Description: Rearrangement of 4 disjuncts. (Contributed by NM, 10-Jan-2005.)

Assertion

Ref	Expression
or42	|- (((ph \/ ps) \/ (ch \/ th)) <-> ((ph \/ ch) \/ (th \/ ps)))

Proof of Theorem or42

Step	Hyp	Ref	Expression
1		or4 514	. 2 |- (((ph \/ ps) \/ (ch \/ th)) <-> ((ph \/ ch) \/ (ps \/ th)))
2		orcom 376	. . 3 |- ((ps \/ th) <-> (th \/ ps))
3	2	orbi2i 505	. 2 |- (((ph \/ ch) \/ (ps \/ th)) <-> ((ph \/ ch) \/ (th \/ ps)))
4	1, 3	bitri 240	1 |- (((ph \/ ps) \/ (ch \/ th)) <-> ((ph \/ ch) \/ (th \/ 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: (None)