Theorem 3mix3 1115

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 1113	. 2 |- ( ph -> ( ph \/ ps \/ ch ) )
2		3orrot 931	. 2 |- ( ( ph \/ ps \/ ch ) <-> ( ps \/ ch \/ ph ) )
3	1, 2	sylib 121	1 |- ( ph -> ( ps \/ ch \/ ph ) )

Syntax hints:   -> wi 4   \/ w3o 924

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666

This theorem depends on definitions:  df-bi 116  df-3or 926

This theorem is referenced by:  3mix3i  1118  3mix3d  1121  3jaob  1239  tpid3g  3563  funtpg  5080  nn01to3  9165  fztri3or  9516  qbtwnxr  9732  hashfiv01gt1  10253