Metamath Proof Explorer

Theorem 3orel13

Description: Elimination of two disjuncts in a triple disjunction. (Contributed by Scott Fenton, 9-Jun-2011)

Ref Expression
Assertion 3orel13 
|- ( ( -. ph /\ -. ch ) -> ( ( ph \/ ps \/ ch ) -> ps ) )

Proof

Step Hyp Ref Expression
1 3orel3 
 |-  ( -. ch -> ( ( ph \/ ps \/ ch ) -> ( ph \/ ps ) ) )
2 orel1 
 |-  ( -. ph -> ( ( ph \/ ps ) -> ps ) )
3 1 2 sylan9r 
 |-  ( ( -. ph /\ -. ch ) -> ( ( ph \/ ps \/ ch ) -> ps ) )