Theorem or4 514

Description: Rearrangement of 4 disjuncts. (Contributed by NM, 12-Aug-1994.)

Assertion

Ref	Expression
or4	|- (((ph \/ ps) \/ (ch \/ th)) <-> ((ph \/ ch) \/ (ps \/ th)))

Proof of Theorem or4

Step	Hyp	Ref	Expression
1		or12 509	. . 3 |- ((ps \/ (ch \/ th)) <-> (ch \/ (ps \/ th)))
2	1	orbi2i 505	. 2 |- ((ph \/ (ps \/ (ch \/ th))) <-> (ph \/ (ch \/ (ps \/ th))))
3		orass 510	. 2 |- (((ph \/ ps) \/ (ch \/ th)) <-> (ph \/ (ps \/ (ch \/ th))))
4		orass 510	. 2 |- (((ph \/ ch) \/ (ps \/ th)) <-> (ph \/ (ch \/ (ps \/ th))))
5	2, 3, 4	3bitr4i 268	1 |- (((ph \/ ps) \/ (ch \/ th)) <-> ((ph \/ ch) \/ (ps \/ th)))

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:  or42  515  orordi  516  orordir  517  3or6  1263