Theorem 3mix1 1151

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 702	. 2 |- ( ph -> ( ph \/ ( ps \/ ch ) ) )
2		3orass 966	. 2 |- ( ( ph \/ ps \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )
3	1, 2	sylibr 133	1 |- ( ph -> ( ph \/ ps \/ ch ) )

Syntax hints:   -> wi 4   \/ wo 698   \/ w3o 962

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699

This theorem depends on definitions:  df-bi 116  df-3or 964

This theorem is referenced by:  3mix2  1152  3mix3  1153  3mix1i  1154  3mix1d  1157  3jaob  1281  nntri3or  6397  elnn0z  9091  nn0le2is012  9157  nn01to3  9436  fztri3or  9850