Theorem 3orass 983

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 981	. 2 |- ( ( ph \/ ps \/ ch ) <-> ( ( ph \/ ps ) \/ ch ) )
2		orass 768	. 2 |- ( ( ( ph \/ ps ) \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )
3	1, 2	bitri 184	1 |- ( ( ph \/ ps \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )

Syntax hints:   <-> wb 105   \/ wo 709   \/ w3o 979

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 710

This theorem depends on definitions:  df-bi 117  df-3or 981

This theorem is referenced by:  3orrot  986  3orcomb  989  3mix1  1168  sotritric  4360  sotritrieq  4361  ordtriexmid  4558  ontriexmidim  4559  acexmidlemcase  5920  nntri3or  6560  nntri2  6561  exmidontriimlem1  7306  elnnz  9355  elznn0  9360  elznn  9361  zapne  9419  nn01to3  9710  elxr  9870  bezoutlemmain  12192  nninfctlemfo  12234  lgsdilem  15376  gausslemma2dlem4  15413