Theorem orass 719

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 682	. 2 |- ( ( ( ph \/ ps ) \/ ch ) <-> ( ch \/ ( ph \/ ps ) ) )
2		or12 718	. 2 |- ( ( ch \/ ( ph \/ ps ) ) <-> ( ph \/ ( ch \/ ps ) ) )
3		orcom 682	. . 3 |- ( ( ch \/ ps ) <-> ( ps \/ ch ) )
4	3	orbi2i 714	. 2 |- ( ( ph \/ ( ch \/ ps ) ) <-> ( ph \/ ( ps \/ ch ) ) )
5	1, 2, 4	3bitri 204	1 |- ( ( ( ph \/ ps ) \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )

Syntax hints:   <-> wb 103   \/ wo 664

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  pm2.31  720  pm2.32  721  or32  722  or4  723  3orass  927  dveeq2  1743  dveeq2or  1744  sbequilem  1766  dvelimALT  1934  dvelimfv  1935  dvelimor  1942  unass  3157  ltxr  9244  lcmass  11341