Theorem or42 265

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 264	. 2 |- (((ph \/ ps) \/ (ch \/ th)) <-> ((ph \/ ch) \/ (ps \/ th)))
2		orcom 246	. . 3 |- ((ps \/ th) <-> (th \/ ps))
3	2	orbi2i 255	. 2 |- (((ph \/ ch) \/ (ps \/ th)) <-> ((ph \/ ch) \/ (th \/ ps)))
4	1, 3	bitr 173	1 |- (((ph \/ ps) \/ (ch \/ th)) <-> ((ph \/ ch) \/ (th \/ ps)))

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

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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