Theorem 3mix2 1167

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

Assertion

Ref	Expression
3mix2	|- ( ph -> ( ps \/ ph \/ ch ) )

Proof of Theorem 3mix2

Step	Hyp	Ref	Expression
1		3mix1 1166	. 2 |- ( ph -> ( ph \/ ch \/ ps ) )
2		3orrot 984	. 2 |- ( ( ps \/ ph \/ ch ) <-> ( ph \/ ch \/ ps ) )
3	1, 2	sylibr 134	1 |- ( ph -> ( ps \/ ph \/ ch ) )

Syntax hints:   -> wi 4   \/ w3o 977

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 709

This theorem depends on definitions:  df-bi 117  df-3or 979

This theorem is referenced by:  3mix2i  1170  3mix2d  1173  3jaob  1302  funtpg  5267  elnn0z  9264  nn0le2is012  9333  nn01to3  9615  zabsle1  14293  triap  14659