Metamath Proof Explorer

Theorem 3orel3

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

Ref Expression
Assertion 3orel3 
|- ( -. ch -> ( ( ph \/ ps \/ ch ) -> ( ph \/ ps ) ) )

Proof

Step Hyp Ref Expression
1 df-3or 
 |-  ( ( ph \/ ps \/ ch ) <-> ( ( ph \/ ps ) \/ ch ) )
2 orel2 
 |-  ( -. ch -> ( ( ( ph \/ ps ) \/ ch ) -> ( ph \/ ps ) ) )
3 1 2 syl5bi 
 |-  ( -. ch -> ( ( ph \/ ps \/ ch ) -> ( ph \/ ps ) ) )