Metamath Proof Explorer

Theorem ltnrd

Description: 'Less than' is irreflexive. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypothesis ltd.1 
|- ( ph -> A e. RR )
Assertion ltnrd 
|- ( ph -> -. A < A )

Proof

Step Hyp Ref Expression
1 ltd.1 
 |-  ( ph -> A e. RR )
2 ltnr 
 |-  ( A e. RR -> -. A < A )
3 1 2 syl 
 |-  ( ph -> -. A < A )