Theorem orass 546

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 402	. 2 |- ( ( ( ph \/ ps ) \/ ch ) <-> ( ch \/ ( ph \/ ps ) ) )
2		or12 545	. 2 |- ( ( ch \/ ( ph \/ ps ) ) <-> ( ph \/ ( ch \/ ps ) ) )
3		orcom 402	. . 3 |- ( ( ch \/ ps ) <-> ( ps \/ ch ) )
4	3	orbi2i 541	. 2 |- ( ( ph \/ ( ch \/ ps ) ) <-> ( ph \/ ( ps \/ ch ) ) )
5	1, 2, 4	3bitri 286	1 |- ( ( ( ph \/ ps ) \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )

Syntax hints:   <-> wb 196   \/ wo 383

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 197  df-or 385

This theorem is referenced by:  pm2.31  547  pm2.32  548  or32  549  or4  550  3orass  1040  axi12  2600  unass  3770  tppreqb  4336  ltxr  11949  lcmass  15327  plydivex  24052  disjxpin  29401  impor  33880  ifpim123g  37845