Metamath Proof Explorer


Theorem lttr

Description: Alias for axlttrn , for naming consistency with lttri . New proofs should generally use this instead of ax-pre-lttrn . (Contributed by NM, 10-Mar-2008)

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

Proof

Step Hyp Ref Expression
1 axlttrn
 |-  ( ( A e. RR /\ B e. RR /\ C e. RR ) -> ( ( A < B /\ B < C ) -> A < C ) )