Theorem readdcli 7885

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 7852	. 2 |- ( ( A e. RR /\ B e. RR ) -> ( A + B ) e. RR )
4	1, 2, 3	mp2an 423	1 |- ( A + B ) e. RR

Syntax hints:   e. wcel 2128  (class class class)co 5821   RRcr 7725   + caddc 7729

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 107  ax-addrcl 7823

This theorem is referenced by:  resubcli  8132  eqneg  8599  2re  8897  3re  8901  4re  8904  5re  8906  6re  8908  7re  8910  8re  8912  9re  8914  numltc  9314  ef01bndlem  11646  ex-fl  13272