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Theorem 7re 8178
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 8159 . 2 7 = (6 + 1)
2 6re 8176 . . 3 6 ∈ ℝ
3 1re 7169 . . 3 1 ∈ ℝ
42, 3readdcli 7183 . 2 (6 + 1) ∈ ℝ
51, 4eqeltri 2152 1 7 ∈ ℝ
Colors of variables: wff set class
Syntax hints:  wcel 1434  (class class class)co 5537  cr 7031  1c1 7033   + caddc 7035  6c6 8149  7c7 8150
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 7121  ax-addrcl 7124
This theorem depends on definitions:  df-bi 115  df-cleq 2075  df-clel 2078  df-2 8154  df-3 8155  df-4 8156  df-5 8157  df-6 8158  df-7 8159
This theorem is referenced by:  7cn  8179  8re  8180  8pos  8198  5lt7  8273  4lt7  8274  3lt7  8275  2lt7  8276  1lt7  8277  7lt8  8278  6lt8  8279  7lt9  8286  6lt9  8287  7lt10  8679  6lt10  8680
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