Theorem ltpnfd

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

	Ref	Expression
Hypothesis	ltpnfd.a	$$⊢\phi \to A\in ℝ$$
Assertion	ltpnfd	$$⊢\phi \to A<\mathrm{+\infty }$$

Proof

Step	Hyp	Ref	Expression
1		ltpnfd.a	$$⊢\phi \to A\in ℝ$$
2		ltpnf	$$⊢A\in ℝ\to A<\mathrm{+\infty }$$
3	1 2	syl	$$⊢\phi \to A<\mathrm{+\infty }$$