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Theorem nn0readdcl 9254
Description: Closure law for addition of reals, restricted to nonnegative integers. (Contributed by Alexander van der Vekens, 6-Apr-2018.)
Assertion
Ref Expression
nn0readdcl  |-  ( ( A  e.  NN0  /\  B  e.  NN0 )  -> 
( A  +  B
)  e.  RR )

Proof of Theorem nn0readdcl
StepHypRef Expression
1 nn0addcl 9230 . 2  |-  ( ( A  e.  NN0  /\  B  e.  NN0 )  -> 
( A  +  B
)  e.  NN0 )
21nn0red 9249 1  |-  ( ( A  e.  NN0  /\  B  e.  NN0 )  -> 
( A  +  B
)  e.  RR )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 104    e. wcel 2160  (class class class)co 5891   RRcr 7829    + caddc 7833   NN0cn0 9195
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171  ax-sep 4136  ax-cnex 7921  ax-resscn 7922  ax-1cn 7923  ax-1re 7924  ax-icn 7925  ax-addcl 7926  ax-addrcl 7927  ax-mulcl 7928  ax-addcom 7930  ax-addass 7932  ax-i2m1 7935  ax-0id 7938  ax-rnegex 7939
This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-ral 2473  df-rex 2474  df-rab 2477  df-v 2754  df-un 3148  df-in 3150  df-ss 3157  df-sn 3613  df-pr 3614  df-op 3616  df-uni 3825  df-int 3860  df-br 4019  df-iota 5193  df-fv 5239  df-ov 5894  df-inn 8939  df-n0 9196
This theorem is referenced by:  difelfznle  10154  facavg  10745
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