Theorem 3mix2 1169

Description: Introduction in triple disjunction. (Contributed by NM, 4-Apr-1995.)

Assertion

Ref	Expression
3mix2	|- ( ph -> ( ps \/ ph \/ ch ) )

Proof of Theorem 3mix2

Step	Hyp	Ref	Expression
1		3mix1 1168	. 2 |- ( ph -> ( ph \/ ch \/ ps ) )
2		3orrot 986	. 2 |- ( ( ps \/ ph \/ ch ) <-> ( ph \/ ch \/ ps ) )
3	1, 2	sylibr 134	1 |- ( ph -> ( ps \/ ph \/ ch ) )

Syntax hints:   -> wi 4   \/ 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:  3mix2i  1172  3mix2d  1175  3jaob  1313  funtpg  5305  elnn0z  9330  nn0le2is012  9399  nn01to3  9682  zabsle1  15115  triap  15519