Metamath Proof Explorer

Theorem 3orel1

Description: Partial elimination of a triple disjunction by denial of a disjunct. (Contributed by Scott Fenton, 26-Mar-2011)

Ref Expression
Assertion 3orel1 
|- ( -. ph -> ( ( ph \/ ps \/ ch ) -> ( ps \/ ch ) ) )

Proof

Step Hyp Ref Expression
1 3orass 
 |-  ( ( ph \/ ps \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )
2 orel1 
 |-  ( -. ph -> ( ( ph \/ ( ps \/ ch ) ) -> ( ps \/ ch ) ) )
3 1 2 syl5bi 
 |-  ( -. ph -> ( ( ph \/ ps \/ ch ) -> ( ps \/ ch ) ) )