Theorem readdcli 8339

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 8305	. 2 |- ( ( A e. RR /\ B e. RR ) -> ( A + B ) e. RR )
4	1, 2, 3	mp2an 430	1 |- ( A + B ) e. RR

This proof depends on syntax axioms:   e. wcel 2209  (class class class)co 6085   RRcr 8178   + caddc 8182

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-addrcl 8276

This theorem is used by:  resubcli  8589  eqneg  9062  2re  9374  3re  9378  4re  9381  5re  9383  6re  9385  7re  9387  8re  9389  9re  9391  numltc  9802  ef01bndlem  12523  ballotfilem2  13228  log2ublog2  16086  ex-fl  16739