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Theorem readdcli 7480
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 7447 . 2  |-  ( ( A  e.  RR  /\  B  e.  RR )  ->  ( A  +  B
)  e.  RR )
41, 2, 3mp2an 417 1  |-  ( A  +  B )  e.  RR
Colors of variables: wff set class
Syntax hints:    e. wcel 1438  (class class class)co 5634   RRcr 7328    + caddc 7332
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 106  ax-addrcl 7421
This theorem is referenced by:  resubcli  7724  eqneg  8173  2re  8463  3re  8467  4re  8470  5re  8472  6re  8474  7re  8476  8re  8478  9re  8480  numltc  8871  ex-fl  11309
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