Theorem archd

Description: Archimedean property of real numbers. For any real number, there is an integer greater than it. Theorem I.29 of Apostol p. 26. (Contributed by Glauco Siliprandi, 1-Feb-2025)

	Ref	Expression
Hypothesis	archd.1	$$⊢\phi \to A\in ℝ$$
Assertion	archd	$$⊢\phi \to \exists n\in \mathbb{N}A<n$$

Proof

Step	Hyp	Ref	Expression
1		archd.1	$$⊢\phi \to A\in ℝ$$
2		arch	$$⊢A\in ℝ\to \exists n\in \mathbb{N}A<n$$
3	1 2	syl	$$⊢\phi \to \exists n\in \mathbb{N}A<n$$