Theorem or12 258

Description: A rearrangement of disjuncts.

Assertion

Ref	Expression
or12	|- ((ph \/ (ps \/ ch)) <-> (ps \/ (ph \/ ch)))

Proof of Theorem or12

Step	Hyp	Ref	Expression
1		bi2.04 160	. . 3 |- ((-. ps -> (-. ph -> ch)) <-> (-. ph -> (-. ps -> ch)))
2		df-or 224	. . . 4 |- ((ph \/ ch) <-> (-. ph -> ch))
3	2	imbi2i 185	. . 3 |- ((-. ps -> (ph \/ ch)) <-> (-. ps -> (-. ph -> ch)))
4		df-or 224	. . . 4 |- ((ps \/ ch) <-> (-. ps -> ch))
5	4	imbi2i 185	. . 3 |- ((-. ph -> (ps \/ ch)) <-> (-. ph -> (-. ps -> ch)))
6	1, 3, 5	3bitr4r 184	. 2 |- ((-. ph -> (ps \/ ch)) <-> (-. ps -> (ph \/ ch)))
7		df-or 224	. 2 |- ((ph \/ (ps \/ ch)) <-> (-. ph -> (ps \/ ch)))
8		df-or 224	. 2 |- ((ps \/ (ph \/ ch)) <-> (-. ps -> (ph \/ ch)))
9	6, 7, 8	3bitr4 183	1 |- ((ph \/ (ps \/ ch)) <-> (ps \/ (ph \/ ch)))

Syntax hints:  -. wn 2   -> wi 3   <-> wb 146   \/ wo 222

This theorem is referenced by:  pm1.5 259  orass 260  or4 264  ordzsl 3106  posex 5856

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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