Theorem or23 270

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 253	. . 3 |- ((ps \/ ch) <-> (ch \/ ps))
2	1	orbi2i 262	. 2 |- ((ph \/ (ps \/ ch)) <-> (ph \/ (ch \/ ps)))
3		orass 267	. 2 |- (((ph \/ ps) \/ ch) <-> (ph \/ (ps \/ ch)))
4		orass 267	. 2 |- (((ph \/ ch) \/ ps) <-> (ph \/ (ch \/ ps)))
5	2, 3, 4	3bitr4i 190	1 |- (((ph \/ ps) \/ ch) <-> ((ph \/ ch) \/ ps))

Syntax hints:   <-> wb 153   \/ wo 229

This theorem is referenced by:  sspsstri 2199  wereu 3002  ordtri3or 3036  ordtri3 3040  psslinpr 5200  xrinfmss 6161

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 154  df-or 231

Copyright terms: Public domain