Metamath Proof Explorer

Theorem ltpnfd

Description: Any (finite) real is less than plus infinity. (Contributed by Glauco Siliprandi, 11-Dec-2019)

Ref Expression
Hypothesis ltpnfd.a 
|- ( ph -> A e. RR )
Assertion ltpnfd 
|- ( ph -> A < +oo )

Proof

Step Hyp Ref Expression
1 ltpnfd.a 
 |-  ( ph -> A e. RR )
2 ltpnf 
 |-  ( A e. RR -> A < +oo )
3 1 2 syl 
 |-  ( ph -> A < +oo )