Theorem pnfged

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

	Ref	Expression
Hypothesis	pnfged.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ* )
Assertion	pnfged	⊢ ( 𝜑 → 𝐴 ≤ +∞ )

Proof

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