Metamath Proof Explorer

Theorem remulcli

Description: Closure law for multiplication of reals. (Contributed by NM, 17-Jan-1997)

Ref Expression
Hypotheses recni.1 
|- A e. RR
axri.2 
|- B e. RR
Assertion remulcli 
|- ( A x. B ) e. RR

Proof

Step Hyp Ref Expression
1 recni.1 
 |-  A e. RR
2 axri.2 
 |-  B e. RR
3 remulcl 
 |-  ( ( A e. RR /\ B e. RR ) -> ( A x. B ) e. RR )
4 1 2 3 mp2an 
 |-  ( A x. B ) e. RR