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Theorem 8re 8419
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 8399 . 2  |-  8  =  ( 7  +  1 )
2 7re 8417 . . 3  |-  7  e.  RR
3 1re 7408 . . 3  |-  1  e.  RR
42, 3readdcli 7422 . 2  |-  ( 7  +  1 )  e.  RR
51, 4eqeltri 2157 1  |-  8  e.  RR
Colors of variables: wff set class
Syntax hints:    e. wcel 1436  (class class class)co 5594   RRcr 7270   1c1 7272    + caddc 7274   7c7 8389   8c8 8390
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 1379  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-4 1443  ax-17 1462  ax-ial 1470  ax-ext 2067  ax-1re 7360  ax-addrcl 7363
This theorem depends on definitions:  df-bi 115  df-cleq 2078  df-clel 2081  df-2 8393  df-3 8394  df-4 8395  df-5 8396  df-6 8397  df-7 8398  df-8 8399
This theorem is referenced by:  8cn  8420  9re  8421  9pos  8438  6lt8  8518  5lt8  8519  4lt8  8520  3lt8  8521  2lt8  8522  1lt8  8523  8lt9  8524  7lt9  8525  8th4div3  8545  8lt10  8917  7lt10  8918
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