Theorem 3mix3 1163

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

Assertion

Ref	Expression
3mix3	|- ( ph -> ( ps \/ ch \/ ph ) )

Proof of Theorem 3mix3

Step	Hyp	Ref	Expression
1		3mix1 1161	. 2 |- ( ph -> ( ph \/ ps \/ ch ) )
2		3orrot 979	. 2 |- ( ( ph \/ ps \/ ch ) <-> ( ps \/ ch \/ ph ) )
3	1, 2	sylib 121	1 |- ( ph -> ( ps \/ ch \/ ph ) )

Syntax hints:   -> wi 4   \/ w3o 972

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 704

This theorem depends on definitions:  df-bi 116  df-3or 974

This theorem is referenced by:  3mix3i  1166  3mix3d  1169  3jaob  1297  tpid3g  3698  funtpg  5249  exmidontriimlem3  7200  nn0le2is012  9294  nn01to3  9576  fztri3or  9995  qbtwnxr  10214  hashfiv01gt1  10716