Theorem ltpnfd

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

	Ref	Expression
Hypothesis	ltpnfd.a	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
Assertion	ltpnfd	⊢ ( 𝜑 → 𝐴 < +∞ )

Proof

Step	Hyp	Ref	Expression
1		ltpnfd.a	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
2		ltpnf	⊢ ( 𝐴 ∈ ℝ → 𝐴 < +∞ )
3	1 2	syl	⊢ ( 𝜑 → 𝐴 < +∞ )