Metamath Proof Explorer

Theorem 3mix1d

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

Ref Expression
Hypothesis 3mixd.1 
|- ( ph -> ps )
Assertion 3mix1d 
|- ( ph -> ( ps \/ ch \/ th ) )

Proof

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