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Theorem 5re 8069
Description: The number 5 is real. (Contributed by NM, 27-May-1999.)
Assertion
Ref Expression
5re 5 ∈ ℝ

Proof of Theorem 5re
StepHypRef Expression
1 df-5 8052 . 2 5 = (4 + 1)
2 4re 8067 . . 3 4 ∈ ℝ
3 1re 7084 . . 3 1 ∈ ℝ
42, 3readdcli 7098 . 2 (4 + 1) ∈ ℝ
51, 4eqeltri 2126 1 5 ∈ ℝ
Colors of variables: wff set class
Syntax hints:  wcel 1409  (class class class)co 5540  cr 6946  1c1 6948   + caddc 6950  4c4 8042  5c5 8043
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 1352  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-4 1416  ax-17 1435  ax-ial 1443  ax-ext 2038  ax-1re 7036  ax-addrcl 7039
This theorem depends on definitions:  df-bi 114  df-cleq 2049  df-clel 2052  df-2 8049  df-3 8050  df-4 8051  df-5 8052
This theorem is referenced by:  5cn  8070  6re  8071  6pos  8091  3lt5  8159  2lt5  8160  1lt5  8161  5lt6  8162  4lt6  8163  5lt7  8168  4lt7  8169  5lt8  8175  4lt8  8176  5lt9  8183  4lt9  8184  5lt10  8561  4lt10  8562
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