Metamath Proof Explorer

Theorem pnfged

Description: Plus infinity is an upper bound for extended reals. (Contributed by Glauco Siliprandi, 5-Feb-2022)

Ref Expression
Hypothesis pnfged.1 
|- ( ph -> A e. RR* )
Assertion pnfged 
|- ( ph -> A <_ +oo )

Proof

Step Hyp Ref Expression
1 pnfged.1 
 |-  ( ph -> A e. RR* )
2 pnfge 
 |-  ( A e. RR* -> A <_ +oo )
3 1 2 syl 
 |-  ( ph -> A <_ +oo )