Theorem or23 263

Description: A rearrangement of disjuncts.

Assertion

Ref	Expression
or23	|- (((ph \/ ps) \/ ch) <-> ((ph \/ ch) \/ ps))

Proof of Theorem or23

Step	Hyp	Ref	Expression
1		orcom 246	. . 3 |- ((ps \/ ch) <-> (ch \/ ps))
2	1	orbi2i 255	. 2 |- ((ph \/ (ps \/ ch)) <-> (ph \/ (ch \/ ps)))
3		orass 260	. 2 |- (((ph \/ ps) \/ ch) <-> (ph \/ (ps \/ ch)))
4		orass 260	. 2 |- (((ph \/ ch) \/ ps) <-> (ph \/ (ch \/ ps)))
5	2, 3, 4	3bitr4 183	1 |- (((ph \/ ps) \/ ch) <-> ((ph \/ ch) \/ ps))

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

This theorem is referenced by:  sspsstri 2148  wereu 2945  ordtri3or 2979  ordtri3 2983  psslinpr 5135  xrinfmss 6079

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

Copyright terms: Public domain