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

Theorem 7re 8815
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 8796 . 2  |-  7  =  ( 6  +  1 )
2 6re 8813 . . 3  |-  6  e.  RR
3 1re 7777 . . 3  |-  1  e.  RR
42, 3readdcli 7791 . 2  |-  ( 6  +  1 )  e.  RR
51, 4eqeltri 2212 1  |-  7  e.  RR
Colors of variables: wff set class
Syntax hints:    e. wcel 1480  (class class class)co 5774   RRcr 7631   1c1 7633    + caddc 7635   6c6 8787   7c7 8788
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 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-17 1506  ax-ial 1514  ax-ext 2121  ax-1re 7726  ax-addrcl 7729
This theorem depends on definitions:  df-bi 116  df-cleq 2132  df-clel 2135  df-2 8791  df-3 8792  df-4 8793  df-5 8794  df-6 8795  df-7 8796
This theorem is referenced by:  7cn  8816  8re  8817  8pos  8835  5lt7  8917  4lt7  8918  3lt7  8919  2lt7  8920  1lt7  8921  7lt8  8922  6lt8  8923  7lt9  8930  6lt9  8931  7lt10  9326  6lt10  9327
  Copyright terms: Public domain W3C validator