Metamath Proof Explorer

Theorem fsumcl

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

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


Step Hyp Ref Expression
1 fsumcl.1 φ A Fin
2 fsumcl.2 φ k A B
3 ssidd φ
4 addcl x y x + y
5 4 adantl φ x y x + y
6 0cnd φ 0
7 3 5 1 2 6 fsumcllem φ k A B