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  4359  sotritrieq  4360  ordtriexmid  4557  ontriexmidim  4558  acexmidlemcase  5917  nntri3or  6551  nntri2  6552  exmidontriimlem1  7288  elnnz  9336  elznn0  9341  elznn  9342  zapne  9400  nn01to3  9691  elxr  9851  bezoutlemmain  12165  nninfctlemfo  12207  lgsdilem  15268  gausslemma2dlem4  15305