Theorem readdcli 7779

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 7746	. 2 |- ( ( A e. RR /\ B e. RR ) -> ( A + B ) e. RR )
4	1, 2, 3	mp2an 422	1 |- ( A + B ) e. RR

Syntax hints:   e. wcel 1480  (class class class)co 5774   RRcr 7619   + caddc 7623

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 107  ax-addrcl 7717

This theorem is referenced by:  resubcli  8025  eqneg  8492  2re  8790  3re  8794  4re  8797  5re  8799  6re  8801  7re  8803  8re  8805  9re  8807  numltc  9207  ef01bndlem  11463  ex-fl  12937