Theorem addcli 8331

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 8305	. 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 6085   CCcc 8178   + caddc 8183

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-addcl 8276

This theorem is used by:  negdii  8612  eqneg  9065  nummac  9831  binom2i  11100  3dvds2dec  12652  mod2xnegi  13221  karatsuba  13233  ballotfilem2  13280  bposlem8  16279