Theorem readdcli 8329

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 8295	. 2 |- ( ( A e. RR /\ B e. RR ) -> ( A + B ) e. RR )
4	1, 2, 3	mp2an 430	1 |- ( A + B ) e. RR

Syntax hints:   e. wcel 2209  (class class class)co 6075   RRcr 8168   + caddc 8172

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-addrcl 8266

This theorem is referenced by:  resubcli  8579  eqneg  9052  2re  9353  3re  9357  4re  9360  5re  9362  6re  9364  7re  9366  8re  9368  9re  9370  numltc  9781  ef01bndlem  12501  ballotfilem2  13206  ex-fl  16653