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Theorem 8re 8045
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 8025 . 2 8 = (7 + 1)
2 7re 8043 . . 3 7 ∈ ℝ
3 1re 7054 . . 3 1 ∈ ℝ
42, 3readdcli 7068 . 2 (7 + 1) ∈ ℝ
51, 4eqeltri 2124 1 8 ∈ ℝ
Colors of variables: wff set class
Syntax hints:  wcel 1407  (class class class)co 5537  cr 6916  1c1 6918   + caddc 6920  7c7 8015  8c8 8016
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1350  ax-gen 1352  ax-ie1 1396  ax-ie2 1397  ax-4 1414  ax-17 1433  ax-ial 1441  ax-ext 2036  ax-1re 7006  ax-addrcl 7009
This theorem depends on definitions:  df-bi 114  df-cleq 2047  df-clel 2050  df-2 8019  df-3 8020  df-4 8021  df-5 8022  df-6 8023  df-7 8024  df-8 8025
This theorem is referenced by:  8cn  8046  9re  8047  9pos  8064  6lt8  8144  5lt8  8145  4lt8  8146  3lt8  8147  2lt8  8148  1lt8  8149  8lt9  8150  7lt9  8151  8th4div3  8171  8lt10  8528  7lt10  8529
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