Theorem readdcli 8287

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 8253	. 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 2203  (class class class)co 6050   RRcr 8126   + caddc 8130

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-addrcl 8224

This theorem is referenced by:  resubcli  8536  eqneg  9006  2re  9307  3re  9311  4re  9314  5re  9316  6re  9318  7re  9320  8re  9322  9re  9324  numltc  9734  ef01bndlem  12442  ballotfilem2  13142  ex-fl  16493