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Theorem 7re 8771
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 8752 . 2 7 = (6 + 1)
2 6re 8769 . . 3 6 ∈ ℝ
3 1re 7733 . . 3 1 ∈ ℝ
42, 3readdcli 7747 . 2 (6 + 1) ∈ ℝ
51, 4eqeltri 2190 1 7 ∈ ℝ
Colors of variables: wff set class
Syntax hints:  wcel 1465  (class class class)co 5742  cr 7587  1c1 7589   + caddc 7591  6c6 8743  7c7 8744
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1408  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-4 1472  ax-17 1491  ax-ial 1499  ax-ext 2099  ax-1re 7682  ax-addrcl 7685
This theorem depends on definitions:  df-bi 116  df-cleq 2110  df-clel 2113  df-2 8747  df-3 8748  df-4 8749  df-5 8750  df-6 8751  df-7 8752
This theorem is referenced by:  7cn  8772  8re  8773  8pos  8791  5lt7  8873  4lt7  8874  3lt7  8875  2lt7  8876  1lt7  8877  7lt8  8878  6lt8  8879  7lt9  8886  6lt9  8887  7lt10  9282  6lt10  9283
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