Theorem orass 769

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 730	. 2 |- ( ( ( ph \/ ps ) \/ ch ) <-> ( ch \/ ( ph \/ ps ) ) )
2		or12 768	. 2 |- ( ( ch \/ ( ph \/ ps ) ) <-> ( ph \/ ( ch \/ ps ) ) )
3		orcom 730	. . 3 |- ( ( ch \/ ps ) <-> ( ps \/ ch ) )
4	3	orbi2i 764	. 2 |- ( ( ph \/ ( ch \/ ps ) ) <-> ( ph \/ ( ps \/ ch ) ) )
5	1, 2, 4	3bitri 206	1 |- ( ( ( ph \/ ps ) \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )

Syntax hints:   <-> wb 105   \/ wo 710

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 711

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  pm2.31  770  pm2.32  771  or32  772  or4  773  3orass  984  dveeq2  1838  dveeq2or  1839  sbequilem  1861  dvelimALT  2038  dvelimfv  2039  dvelimor  2046  unass  3330  ltxr  9897  lcmass  12407