Metamath Proof Explorer

Theorem mulcli

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

Ref Expression
Hypotheses axi.1 
|- A e. CC
axi.2 
|- B e. CC
Assertion mulcli 
|- ( A x. B ) e. CC

Proof

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