Metamath Proof Explorer

Theorem sdomdom

Description: Strict dominance implies dominance. (Contributed by NM, 10-Jun-1998)

Ref Expression
Assertion sdomdom 
|- ( A ~< B -> A ~<_ B )

Proof

Step Hyp Ref Expression
1 brsdom 
 |-  ( A ~< B <-> ( A ~<_ B /\ -. A ~~ B ) )
2 1 simplbi 
 |-  ( A ~< B -> A ~<_ B )