Metamath Proof Explorer

Theorem ord

Description: Deduce implication from disjunction. (Contributed by NM, 18-May-1994)

Ref Expression
Hypothesis ord.1 
|- ( ph -> ( ps \/ ch ) )
Assertion ord 
|- ( ph -> ( -. ps -> ch ) )

Proof

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