Metamath Proof Explorer

Theorem readdcli

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

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

Proof

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