Theorem eluz1i

Description: Membership in an upper set of integers. (Contributed by NM, 5-Sep-2005)

	Ref	Expression
Hypothesis	eluz.1	|- M e. ZZ
Assertion	eluz1i	|- ( N e. ( ZZ>= ` M ) <-> ( N e. ZZ /\ M <_ N ) )

Proof

Step	Hyp	Ref	Expression
1		eluz.1	|- M e. ZZ
2		eluz1	|- ( M e. ZZ -> ( N e. ( ZZ>= ` M ) <-> ( N e. ZZ /\ M <_ N ) ) )
3	1 2	ax-mp	|- ( N e. ( ZZ>= ` M ) <-> ( N e. ZZ /\ M <_ N ) )