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Theorem 9re 8965
Description: The number 9 is real. (Contributed by NM, 27-May-1999.)
Assertion
Ref Expression
9re 9 ∈ ℝ

Proof of Theorem 9re
StepHypRef Expression
1 df-9 8944 . 2 9 = (8 + 1)
2 8re 8963 . . 3 8 ∈ ℝ
3 1re 7919 . . 3 1 ∈ ℝ
42, 3readdcli 7933 . 2 (8 + 1) ∈ ℝ
51, 4eqeltri 2243 1 9 ∈ ℝ
Colors of variables: wff set class
Syntax hints:  wcel 2141  (class class class)co 5853  cr 7773  1c1 7775   + caddc 7777  8c8 8935  9c9 8936
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 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-17 1519  ax-ial 1527  ax-ext 2152  ax-1re 7868  ax-addrcl 7871
This theorem depends on definitions:  df-bi 116  df-cleq 2163  df-clel 2166  df-2 8937  df-3 8938  df-4 8939  df-5 8940  df-6 8941  df-7 8942  df-8 8943  df-9 8944
This theorem is referenced by:  9cn  8966  7lt9  9076  6lt9  9077  5lt9  9078  4lt9  9079  3lt9  9080  2lt9  9081  1lt9  9082  9lt10  9473  8lt10  9474  0.999...  11484  cos2bnd  11723  sincos2sgn  11728  setsmsdsg  13274  2logb9irr  13683  2logb9irrap  13689
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