Metamath Proof Explorer

Theorem ltle

Description: 'Less than' implies 'less than or equal to'. (Contributed by NM, 25-Aug-1999)

Ref Expression
Assertion ltle 
|- ( ( A e. RR /\ B e. RR ) -> ( A < B -> A <_ B ) )

Proof

Step Hyp Ref Expression
1 orc 
 |-  ( A < B -> ( A < B \/ A = B ) )
2 leloe 
 |-  ( ( A e. RR /\ B e. RR ) -> ( A <_ B <-> ( A < B \/ A = B ) ) )
3 1 2 imbitrrid 
 |-  ( ( A e. RR /\ B e. RR ) -> ( A < B -> A <_ B ) )