Theorem 3orass 981

Description: Associative law for triple disjunction. (Contributed by NM, 8-Apr-1994.)

Assertion

Ref	Expression
3orass	|- ( ( ph \/ ps \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )

Proof of Theorem 3orass

Step	Hyp	Ref	Expression
1		df-3or 979	. 2 |- ( ( ph \/ ps \/ ch ) <-> ( ( ph \/ ps ) \/ ch ) )
2		orass 767	. 2 |- ( ( ( ph \/ ps ) \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )
3	1, 2	bitri 184	1 |- ( ( ph \/ ps \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )

Syntax hints:   <-> wb 105   \/ wo 708   \/ w3o 977

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 709

This theorem depends on definitions:  df-bi 117  df-3or 979

This theorem is referenced by:  3orrot  984  3orcomb  987  3mix1  1166  sotritric  4324  sotritrieq  4325  ordtriexmid  4520  ontriexmidim  4521  acexmidlemcase  5869  nntri3or  6493  nntri2  6494  exmidontriimlem1  7219  elnnz  9261  elznn0  9266  elznn  9267  zapne  9325  nn01to3  9615  elxr  9774  bezoutlemmain  11993  lgsdilem  14321