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Theorem 7re 8568
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 8549 . 2 7 = (6 + 1)
2 6re 8566 . . 3 6 ∈ ℝ
3 1re 7550 . . 3 1 ∈ ℝ
42, 3readdcli 7564 . 2 (6 + 1) ∈ ℝ
51, 4eqeltri 2161 1 7 ∈ ℝ
Colors of variables: wff set class
Syntax hints:  wcel 1439  (class class class)co 5668  cr 7412  1c1 7414   + caddc 7416  6c6 8540  7c7 8541
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1382  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-4 1446  ax-17 1465  ax-ial 1473  ax-ext 2071  ax-1re 7502  ax-addrcl 7505
This theorem depends on definitions:  df-bi 116  df-cleq 2082  df-clel 2085  df-2 8544  df-3 8545  df-4 8546  df-5 8547  df-6 8548  df-7 8549
This theorem is referenced by:  7cn  8569  8re  8570  8pos  8588  5lt7  8664  4lt7  8665  3lt7  8666  2lt7  8667  1lt7  8668  7lt8  8669  6lt8  8670  7lt9  8677  6lt9  8678  7lt10  9072  6lt10  9073
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