Theorem addcli 8336

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 8310	. 2 |- ( ( A e. CC /\ B e. CC ) -> ( A + B ) e. CC )
4	1, 2, 3	mp2an 430	1 |- ( A + B ) e. CC

This proof depends on syntax axioms:   e. wcel 2209  (class class class)co 6088   CCcc 8183   + caddc 8188

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-addcl 8281

This theorem is used by:  negdii  8617  eqneg  9070  nummac  9837  binom2i  11106  3dvds2dec  12658  mod2xnegi  13227  karatsuba  13239  ballotfilem2  13286  bposlem8  16318