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 ( 𝜑𝐴 ∈ ℝ* )
Assertion pnfged ( 𝜑𝐴 ≤ +∞ )

Proof

Step Hyp Ref Expression
1 pnfged.1 ( 𝜑𝐴 ∈ ℝ* )
2 pnfge ( 𝐴 ∈ ℝ*𝐴 ≤ +∞ )
3 1 2 syl ( 𝜑𝐴 ≤ +∞ )