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Theorem 7re 7998
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 7978 . 2 7 = (6 + 1)
2 6re 7996 . . 3 6 ∈ ℝ
3 1re 7026 . . 3 1 ∈ ℝ
42, 3readdcli 7040 . 2 (6 + 1) ∈ ℝ
51, 4eqeltri 2110 1 7 ∈ ℝ
Colors of variables: wff set class
Syntax hints:  wcel 1393  (class class class)co 5512  cr 6888  1c1 6890   + caddc 6892  6c6 7968  7c7 7969
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427  ax-ext 2022  ax-1re 6978  ax-addrcl 6981
This theorem depends on definitions:  df-bi 110  df-cleq 2033  df-clel 2036  df-2 7973  df-3 7974  df-4 7975  df-5 7976  df-6 7977  df-7 7978
This theorem is referenced by:  7cn  7999  8re  8000  8pos  8019  5lt7  8102  4lt7  8103  3lt7  8104  2lt7  8105  1lt7  8106  7lt8  8107  6lt8  8108  7lt9  8115  6lt9  8116  7lt10  8124  6lt10  8125
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