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Theorem readdcli 7970
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
StepHypRef Expression
1 recni.1 . 2  |-  A  e.  RR
2 axri.2 . 2  |-  B  e.  RR
3 readdcl 7937 . 2  |-  ( ( A  e.  RR  /\  B  e.  RR )  ->  ( A  +  B
)  e.  RR )
41, 2, 3mp2an 426 1  |-  ( A  +  B )  e.  RR
Colors of variables: wff set class
Syntax hints:    e. wcel 2148  (class class class)co 5875   RRcr 7810    + caddc 7814
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-addrcl 7908
This theorem is referenced by:  resubcli  8220  eqneg  8689  2re  8989  3re  8993  4re  8996  5re  8998  6re  9000  7re  9002  8re  9004  9re  9006  numltc  9409  ef01bndlem  11764  ex-fl  14480
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