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Theorem 8re 8478
Description: The number 8 is real. (Contributed by NM, 27-May-1999.)
Assertion
Ref Expression
8re  |-  8  e.  RR

Proof of Theorem 8re
StepHypRef Expression
1 df-8 8458 . 2  |-  8  =  ( 7  +  1 )
2 7re 8476 . . 3  |-  7  e.  RR
3 1re 7466 . . 3  |-  1  e.  RR
42, 3readdcli 7480 . 2  |-  ( 7  +  1 )  e.  RR
51, 4eqeltri 2160 1  |-  8  e.  RR
Colors of variables: wff set class
Syntax hints:    e. wcel 1438  (class class class)co 5634   RRcr 7328   1c1 7330    + caddc 7332   7c7 8449   8c8 8450
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-17 1464  ax-ial 1472  ax-ext 2070  ax-1re 7418  ax-addrcl 7421
This theorem depends on definitions:  df-bi 115  df-cleq 2081  df-clel 2084  df-2 8452  df-3 8453  df-4 8454  df-5 8455  df-6 8456  df-7 8457  df-8 8458
This theorem is referenced by:  8cn  8479  9re  8480  9pos  8497  6lt8  8577  5lt8  8578  4lt8  8579  3lt8  8580  2lt8  8581  1lt8  8582  8lt9  8583  7lt9  8584  8th4div3  8605  8lt10  8977  7lt10  8978
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