Theorem 3mix3d 1169

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

Hypothesis

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

Assertion

Ref	Expression
3mix3d	|- ( ph -> ( ch \/ th \/ ps ) )

Proof of Theorem 3mix3d

Step	Hyp	Ref	Expression
1		3mixd.1	. 2 |- ( ph -> ps )
2		3mix3 1163	. 2 |- ( ps -> ( ch \/ th \/ ps ) )
3	1, 2	syl 14	1 |- ( ph -> ( ch \/ th \/ ps ) )

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:  nnnegz  9215  prm23ge5  12218  zabsle1  13694  trirec0  14076