Theorem 3mix2 1170

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 1169	. 2 |- ( ph -> ( ph \/ ch \/ ps ) )
2		3orrot 987	. 2 |- ( ( ps \/ ph \/ ch ) <-> ( ph \/ ch \/ ps ) )
3	1, 2	sylibr 134	1 |- ( ph -> ( ps \/ ph \/ ch ) )

Syntax hints:   -> wi 4   \/ w3o 980

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  df-3or 982

This theorem is referenced by:  3mix2i  1173  3mix2d  1176  3jaob  1315  funtpg  5325  elnn0z  9385  nn0le2is012  9455  nn01to3  9738  zabsle1  15476  triap  15972