Theorem orass 510

Description: Associative law for disjunction. Theorem *4.33 of [WhiteheadRussell] p. 118. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)

Assertion

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

Proof of Theorem orass

Step	Hyp	Ref	Expression
1		orcom 376	. 2 |- (((ph \/ ps) \/ ch) <-> (ch \/ (ph \/ ps)))
2		or12 509	. 2 |- ((ch \/ (ph \/ ps)) <-> (ph \/ (ch \/ ps)))
3		orcom 376	. . 3 |- ((ch \/ ps) <-> (ps \/ ch))
4	3	orbi2i 505	. 2 |- ((ph \/ (ch \/ ps)) <-> (ph \/ (ps \/ ch)))
5	1, 2, 4	3bitri 262	1 |- (((ph \/ ps) \/ ch) <-> (ph \/ (ps \/ ch)))

Syntax hints:   <-> wb 176   \/ wo 357

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-or 359

This theorem is referenced by:  pm2.31  511  pm2.32  512  or32  513  or4  514  3orass  937  axi12  2333  unass  3421