Theorem or4 264

Description: Rearrangement of 4 disjuncts.

Assertion

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

Proof of Theorem or4

Step	Hyp	Ref	Expression
1		or12 258	. . 3 |- ((ps \/ (ch \/ th)) <-> (ch \/ (ps \/ th)))
2	1	orbi2i 255	. 2 |- ((ph \/ (ps \/ (ch \/ th))) <-> (ph \/ (ch \/ (ps \/ th))))
3		orass 260	. 2 |- (((ph \/ ps) \/ (ch \/ th)) <-> (ph \/ (ps \/ (ch \/ th))))
4		orass 260	. 2 |- (((ph \/ ch) \/ (ps \/ th)) <-> (ph \/ (ch \/ (ps \/ th))))
5	2, 3, 4	3bitr4 183	1 |- (((ph \/ ps) \/ (ch \/ th)) <-> ((ph \/ ch) \/ (ps \/ th)))

Syntax hints:   <-> wb 146   \/ wo 222

This theorem is referenced by:  or42 265  orordi 266  orordir 267  ccase 757  ccased 758

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-or 224

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