Theorem 3mix1 1169

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

Assertion

Ref	Expression
3mix1	|- ( ph -> ( ph \/ ps \/ ch ) )

Proof of Theorem 3mix1

Step	Hyp	Ref	Expression
1		orc 714	. 2 |- ( ph -> ( ph \/ ( ps \/ ch ) ) )
2		3orass 984	. 2 |- ( ( ph \/ ps \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )
3	1, 2	sylibr 134	1 |- ( ph -> ( ph \/ ps \/ ch ) )

Syntax hints:   -> wi 4   \/ wo 710   \/ 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:  3mix2  1170  3mix3  1171  3mix1i  1172  3mix1d  1175  3jaob  1315  nntri3or  6581  exmidontriimlem3  7337  elnn0z  9387  nn0le2is012  9457  nn01to3  9740  fztri3or  10163  zabsle1  15509