Theorem 3mix1 1167

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 713	. 2 |- ( ph -> ( ph \/ ( ps \/ ch ) ) )
2		3orass 982	. 2 |- ( ( ph \/ ps \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )
3	1, 2	sylibr 134	1 |- ( ph -> ( ph \/ ps \/ ch ) )

Syntax hints:   -> wi 4   \/ wo 709   \/ w3o 978

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 980

This theorem is referenced by:  3mix2  1168  3mix3  1169  3mix1i  1170  3mix1d  1173  3jaob  1312  nntri3or  6507  exmidontriimlem3  7235  elnn0z  9279  nn0le2is012  9348  nn01to3  9630  fztri3or  10052  zabsle1  14671