Metamath Proof Explorer

Theorem ltex

Description: The less-than relation is a set. (Contributed by SN, 5-Jun-2025)

Ref Expression
Assertion ltex 
|- < e. _V

Proof

Step Hyp Ref Expression
1 xrex 
 |-  RR* e. _V
2 1 1 xpex 
 |-  ( RR* X. RR* ) e. _V
3 ltrelxr 
 |-  < C_ ( RR* X. RR* )
4 2 3 ssexi 
 |-  < e. _V