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Theorem 8re 8191
Description: The number 8 is real. (Contributed by NM, 27-May-1999.)
Assertion
Ref Expression
8re 8 ∈ ℝ

Proof of Theorem 8re
StepHypRef Expression
1 df-8 8171 . 2 8 = (7 + 1)
2 7re 8189 . . 3 7 ∈ ℝ
3 1re 7180 . . 3 1 ∈ ℝ
42, 3readdcli 7194 . 2 (7 + 1) ∈ ℝ
51, 4eqeltri 2152 1 8 ∈ ℝ
Colors of variables: wff set class
Syntax hints:  wcel 1434  (class class class)co 5543  cr 7042  1c1 7044   + caddc 7046  7c7 8161  8c8 8162
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-17 1460  ax-ial 1468  ax-ext 2064  ax-1re 7132  ax-addrcl 7135
This theorem depends on definitions:  df-bi 115  df-cleq 2075  df-clel 2078  df-2 8165  df-3 8166  df-4 8167  df-5 8168  df-6 8169  df-7 8170  df-8 8171
This theorem is referenced by:  8cn  8192  9re  8193  9pos  8210  6lt8  8290  5lt8  8291  4lt8  8292  3lt8  8293  2lt8  8294  1lt8  8295  8lt9  8296  7lt9  8297  8th4div3  8317  8lt10  8689  7lt10  8690
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