Theorem addcli 8183

Description: Closure law for addition. (Contributed by NM, 23-Nov-1994.)

Hypotheses

Ref	Expression
axi.1	|- A e. CC
axi.2	|- B e. CC

Assertion

Ref	Expression
addcli	|- ( A + B ) e. CC

Proof of Theorem addcli

Step	Hyp	Ref	Expression
1		axi.1	. 2 |- A e. CC
2		axi.2	. 2 |- B e. CC
3		addcl 8157	. 2 |- ( ( A e. CC /\ B e. CC ) -> ( A + B ) e. CC )
4	1, 2, 3	mp2an 426	1 |- ( A + B ) e. CC

Syntax hints:   e. wcel 2202  (class class class)co 6018   CCcc 8030   + caddc 8035

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-addcl 8128

This theorem is referenced by:  negdii  8463  eqneg  8912  nummac  9655  binom2i  10911  3dvds2dec  12432  karatsuba  13008