Metamath Proof Explorer

Theorem fsumzcl

Description: Closure of a finite sum of integers. (Contributed by NM, 9-Nov-2005) (Revised by Mario Carneiro, 22-Apr-2014)

Ref Expression
Hypotheses fsumcl.1 φ A Fin
fsumzcl.2 φ k A B
Assertion fsumzcl φ k A B


Step Hyp Ref Expression
1 fsumcl.1 φ A Fin
2 fsumzcl.2 φ k A B
3 zsscn
4 3 a1i φ
5 zaddcl x y x + y
6 5 adantl φ x y x + y
7 0zd φ 0
8 4 6 1 2 7 fsumcllem φ k A B