Theorem 3mix1 1113

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 669	. 2 |- ( ph -> ( ph \/ ( ps \/ ch ) ) )
2		3orass 928	. 2 |- ( ( ph \/ ps \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )
3	1, 2	sylibr 133	1 |- ( ph -> ( ph \/ ps \/ ch ) )

Syntax hints:   -> wi 4   \/ wo 665   \/ 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:  3mix2  1114  3mix3  1115  3mix1i  1116  3mix1d  1119  3jaob  1239  nntri3or  6270  elnn0z  8826  nn01to3  9165  fztri3or  9516