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Theorem 10re 8004
 Description: The number 10 is real. (Contributed by NM, 5-Feb-2007.)
Assertion
Ref Expression
10re 10 ∈ ℝ

Proof of Theorem 10re
StepHypRef Expression
1 df-10 7981 . 2 10 = (9 + 1)
2 9re 8002 . . 3 9 ∈ ℝ
3 1re 7026 . . 3 1 ∈ ℝ
42, 3readdcli 7040 . 2 (9 + 1) ∈ ℝ
51, 4eqeltri 2110 1 10 ∈ ℝ
 Colors of variables: wff set class Syntax hints:   ∈ wcel 1393  (class class class)co 5512  ℝcr 6888  1c1 6890   + caddc 6892  9c9 7971  10c10 7972 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  df-8 7979  df-9 7980  df-10 7981 This theorem is referenced by:  8lt10  8123  7lt10  8124  6lt10  8125  5lt10  8126  4lt10  8127  3lt10  8128  2lt10  8129  1lt10  8130
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