Theorem 3mix3 1195

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 1193	. 2 |- ( ph -> ( ph \/ ps \/ ch ) )
2		3orrot 1011	. 2 |- ( ( ph \/ ps \/ ch ) <-> ( ps \/ ch \/ ph ) )
3	1, 2	sylib 122	1 |- ( ph -> ( ps \/ ch \/ ph ) )

Syntax hints:   -> wi 4   \/ w3o 1004

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 717

This theorem depends on definitions:  df-bi 117  df-3or 1006

This theorem is referenced by:  3mix3i  1198  3mix3d  1201  3jaob  1339  tpid3g  3791  funtpg  5388  exmidontriimlem3  7498  nn0le2is012  9623  nn01to3  9912  fztri3or  10336  qbtwnxr  10580  hashfiv01gt1  11107  pfxnd  11336  pfxwrdsymbg  11337