Theorem orass 757

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 718	. 2 |- ( ( ( ph \/ ps ) \/ ch ) <-> ( ch \/ ( ph \/ ps ) ) )
2		or12 756	. 2 |- ( ( ch \/ ( ph \/ ps ) ) <-> ( ph \/ ( ch \/ ps ) ) )
3		orcom 718	. . 3 |- ( ( ch \/ ps ) <-> ( ps \/ ch ) )
4	3	orbi2i 752	. 2 |- ( ( ph \/ ( ch \/ ps ) ) <-> ( ph \/ ( ps \/ ch ) ) )
5	1, 2, 4	3bitri 205	1 |- ( ( ( ph \/ ps ) \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )

Syntax hints:   <-> wb 104   \/ wo 698

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  pm2.31  758  pm2.32  759  or32  760  or4  761  3orass  966  dveeq2  1788  dveeq2or  1789  sbequilem  1811  dvelimALT  1986  dvelimfv  1987  dvelimor  1994  unass  3238  ltxr  9592  lcmass  11802