Theorem 3mix1 1166

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 712	. 2 |- ( ph -> ( ph \/ ( ps \/ ch ) ) )
2		3orass 981	. 2 |- ( ( ph \/ ps \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )
3	1, 2	sylibr 134	1 |- ( ph -> ( ph \/ ps \/ ch ) )

Syntax hints:   -> wi 4   \/ wo 708   \/ w3o 977

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 709

This theorem depends on definitions:  df-bi 117  df-3or 979

This theorem is referenced by:  3mix2  1167  3mix3  1168  3mix1i  1169  3mix1d  1172  3jaob  1302  nntri3or  6496  exmidontriimlem3  7224  elnn0z  9268  nn0le2is012  9337  nn01to3  9619  fztri3or  10041  zabsle1  14485