Theorem 3mix1 1107

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 665	. 2 |- ( ph -> ( ph \/ ( ps \/ ch ) ) )
2		3orass 922	. 2 |- ( ( ph \/ ps \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )
3	1, 2	sylibr 132	1 |- ( ph -> ( ph \/ ps \/ ch ) )

Syntax hints:   -> wi 4   \/ wo 661   \/ w3o 918

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662

This theorem depends on definitions:  df-bi 115  df-3or 920

This theorem is referenced by:  3mix2  1108  3mix3  1109  3mix1i  1110  3mix1d  1113  3jaob  1233  nntri3or  6095  elnn0z  8364  nn01to3  8702  fztri3or  9058