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Theorem 7re 9020
Description: The number 7 is real. (Contributed by NM, 27-May-1999.)
Assertion
Ref Expression
7re 7 ∈ ℝ

Proof of Theorem 7re
StepHypRef Expression
1 df-7 9001 . 2 7 = (6 + 1)
2 6re 9018 . . 3 6 ∈ ℝ
3 1re 7974 . . 3 1 ∈ ℝ
42, 3readdcli 7988 . 2 (6 + 1) ∈ ℝ
51, 4eqeltri 2262 1 7 ∈ ℝ
Colors of variables: wff set class
Syntax hints:  wcel 2160  (class class class)co 5891  cr 7828  1c1 7830   + caddc 7832  6c6 8992  7c7 8993
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-5 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-17 1537  ax-ial 1545  ax-ext 2171  ax-1re 7923  ax-addrcl 7926
This theorem depends on definitions:  df-bi 117  df-cleq 2182  df-clel 2185  df-2 8996  df-3 8997  df-4 8998  df-5 8999  df-6 9000  df-7 9001
This theorem is referenced by:  7cn  9021  8re  9022  8pos  9040  5lt7  9122  4lt7  9123  3lt7  9124  2lt7  9125  1lt7  9126  7lt8  9127  6lt8  9128  7lt9  9135  6lt9  9136  7lt10  9534  6lt10  9535  lgsdir2lem1  14813
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