Theorem mulcli 7032

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

Hypotheses

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

Assertion

Ref	Expression
mulcli	|- ( A x. B ) e. CC

Proof of Theorem mulcli

Step	Hyp	Ref	Expression
1		axi.1	. 2 |- A e. CC
2		axi.2	. 2 |- B e. CC
3		mulcl 7008	. 2 |- ( ( A e. CC /\ B e. CC ) -> ( A x. B ) e. CC )
4	1, 2, 3	mp2an 402	1 |- ( A x. B ) e. CC

Syntax hints:   e. wcel 1393  (class class class)co 5512   CCcc 6887   x. cmul 6894

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 101  ax-mulcl 6982

This theorem is referenced by:  ixi  7574  2mulicn  8147  numma  8398  nummac  8399  decbin2  8471  irec  9352  binom2i  9360  rei  9499  imi  9500