ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  7re Unicode version

Theorem 7re 8603
Description: The number 7 is real. (Contributed by NM, 27-May-1999.)
Assertion
Ref Expression
7re  |-  7  e.  RR

Proof of Theorem 7re
StepHypRef Expression
1 df-7 8584 . 2  |-  7  =  ( 6  +  1 )
2 6re 8601 . . 3  |-  6  e.  RR
3 1re 7584 . . 3  |-  1  e.  RR
42, 3readdcli 7598 . 2  |-  ( 6  +  1 )  e.  RR
51, 4eqeltri 2167 1  |-  7  e.  RR
Colors of variables: wff set class
Syntax hints:    e. wcel 1445  (class class class)co 5690   RRcr 7446   1c1 7448    + caddc 7450   6c6 8575   7c7 8576
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1388  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-4 1452  ax-17 1471  ax-ial 1479  ax-ext 2077  ax-1re 7536  ax-addrcl 7539
This theorem depends on definitions:  df-bi 116  df-cleq 2088  df-clel 2091  df-2 8579  df-3 8580  df-4 8581  df-5 8582  df-6 8583  df-7 8584
This theorem is referenced by:  7cn  8604  8re  8605  8pos  8623  5lt7  8699  4lt7  8700  3lt7  8701  2lt7  8702  1lt7  8703  7lt8  8704  6lt8  8705  7lt9  8712  6lt9  8713  7lt10  9108  6lt10  9109
  Copyright terms: Public domain W3C validator