Theorem or4 220

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 217	. . 3 |- ((ps \/ (ch \/ th)) <-> (ch \/ (ps \/ th)))
2	1	orbi2i 214	. 2 |- ((ph \/ (ps \/ (ch \/ th))) <-> (ph \/ (ch \/ (ps \/ th))))
3		orass 218	. 2 |- (((ph \/ ps) \/ (ch \/ th)) <-> (ph \/ (ps \/ (ch \/ th))))
4		orass 218	. 2 |- (((ph \/ ch) \/ (ps \/ th)) <-> (ph \/ (ch \/ (ps \/ th))))
5	2, 3, 4	3bitr4 158	1 |- (((ph \/ ps) \/ (ch \/ th)) <-> ((ph \/ ch) \/ (ps \/ th)))

Syntax hints:   <-> wb 127   \/ wo 195

This theorem is referenced by:  or42 221  orordi 222  orordir 223  ordtri3or 2230

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

This theorem depends on definitions:  df-bi 128  df-or 197

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