Theorem 3mix1d 1167

Description: Deduction introducing triple disjunction. (Contributed by Scott Fenton, 8-Jun-2011.)

Hypothesis

Ref	Expression
3mixd.1	|- ( ph -> ps )

Assertion

Ref	Expression
3mix1d	|- ( ph -> ( ps \/ ch \/ th ) )

Proof of Theorem 3mix1d

Step	Hyp	Ref	Expression
1		3mixd.1	. 2 |- ( ph -> ps )
2		3mix1 1161	. 2 |- ( ps -> ( ps \/ ch \/ th ) )
3	1, 2	syl 14	1 |- ( ph -> ( ps \/ ch \/ th ) )

Syntax hints:   -> wi 4   \/ w3o 972

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704

This theorem depends on definitions:  df-bi 116  df-3or 974

This theorem is referenced by:  trirec0  14076