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Theorem 8re 8000
Description: The number 8 is real. (Contributed by NM, 27-May-1999.)
Assertion
Ref Expression
8re 8 ∈ ℝ

Proof of Theorem 8re
StepHypRef Expression
1 df-8 7979 . 2 8 = (7 + 1)
2 7re 7998 . . 3 7 ∈ ℝ
3 1re 7026 . . 3 1 ∈ ℝ
42, 3readdcli 7040 . 2 (7 + 1) ∈ ℝ
51, 4eqeltri 2110 1 8 ∈ ℝ
Colors of variables: wff set class
Syntax hints:  wcel 1393  (class class class)co 5512  cr 6888  1c1 6890   + caddc 6892  7c7 7969  8c8 7970
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427  ax-ext 2022  ax-1re 6978  ax-addrcl 6981
This theorem depends on definitions:  df-bi 110  df-cleq 2033  df-clel 2036  df-2 7973  df-3 7974  df-4 7975  df-5 7976  df-6 7977  df-7 7978  df-8 7979
This theorem is referenced by:  8cn  8001  9re  8002  9pos  8020  6lt8  8108  5lt8  8109  4lt8  8110  3lt8  8111  2lt8  8112  1lt8  8113  8lt9  8114  7lt9  8115  8lt10  8123  7lt10  8124  8th4div3  8144
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