Theorem or42 221

Description: Rearrangement of 4 disjuncts.

Assertion

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

Proof of Theorem or42

Step	Hyp	Ref	Expression
1		or4 220	. 2 |- (((ph \/ ps) \/ (ch \/ th)) <-> ((ph \/ ch) \/ (ps \/ th)))
2		orcom 209	. . 3 |- ((ps \/ th) <-> (th \/ ps))
3	2	orbi2i 214	. 2 |- (((ph \/ ch) \/ (ps \/ th)) <-> ((ph \/ ch) \/ (th \/ ps)))
4	1, 3	bitr 151	1 |- (((ph \/ ps) \/ (ch \/ th)) <-> ((ph \/ ch) \/ (th \/ ps)))

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

This theorem is referenced by:  biass 511

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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