Theorem readdcli 7984

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

Hypotheses

Ref	Expression
recni.1	|- A e. RR
axri.2	|- B e. RR

Assertion

Ref	Expression
readdcli	|- ( A + B ) e. RR

Proof of Theorem readdcli

Step	Hyp	Ref	Expression
1		recni.1	. 2 |- A e. RR
2		axri.2	. 2 |- B e. RR
3		readdcl 7951	. 2 |- ( ( A e. RR /\ B e. RR ) -> ( A + B ) e. RR )
4	1, 2, 3	mp2an 426	1 |- ( A + B ) e. RR

Syntax hints:   e. wcel 2158  (class class class)co 5888   RRcr 7824   + caddc 7828

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-addrcl 7922

This theorem is referenced by:  resubcli  8234  eqneg  8703  2re  9003  3re  9007  4re  9010  5re  9012  6re  9014  7re  9016  8re  9018  9re  9020  numltc  9423  ef01bndlem  11778  ex-fl  14773