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	|- ( ph -> A e. RR )
Assertion	archd	|- ( ph -> E. n e. NN A < n )

Proof

Step	Hyp	Ref	Expression
1		archd.1	|- ( ph -> A e. RR )
2		arch	|- ( A e. RR -> E. n e. NN A < n )
3	1 2	syl	|- ( ph -> E. n e. NN A < n )