Theorem readdcli 7651

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 7618	. 2 |- ( ( A e. RR /\ B e. RR ) -> ( A + B ) e. RR )
4	1, 2, 3	mp2an 420	1 |- ( A + B ) e. RR

Syntax hints:   e. wcel 1448  (class class class)co 5706   RRcr 7499   + caddc 7503

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 107  ax-addrcl 7592

This theorem is referenced by:  resubcli  7896  eqneg  8353  2re  8648  3re  8652  4re  8655  5re  8657  6re  8659  7re  8661  8re  8663  9re  8665  numltc  9059  ef01bndlem  11261  ex-fl  12540