Theorem pnfged

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

	Ref	Expression
Hypothesis	pnfged.1	$$⊢\phi \to A\in {ℝ}^{*}$$
Assertion	pnfged	$$⊢\phi \to A\le \mathrm{+\infty }$$

Proof

Step	Hyp	Ref	Expression
1		pnfged.1	$$⊢\phi \to A\in {ℝ}^{*}$$
2		pnfge	$$⊢A\in {ℝ}^{*}\to A\le \mathrm{+\infty }$$
3	1 2	syl	$$⊢\phi \to A\le \mathrm{+\infty }$$