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

Theorem 7re 9073
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 9054 . 2  |-  7  =  ( 6  +  1 )
2 6re 9071 . . 3  |-  6  e.  RR
3 1re 8025 . . 3  |-  1  e.  RR
42, 3readdcli 8039 . 2  |-  ( 6  +  1 )  e.  RR
51, 4eqeltri 2269 1  |-  7  e.  RR
Colors of variables: wff set class
Syntax hints:    e. wcel 2167  (class class class)co 5922   RRcr 7878   1c1 7880    + caddc 7882   6c6 9045   7c7 9046
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1461  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-4 1524  ax-17 1540  ax-ial 1548  ax-ext 2178  ax-1re 7973  ax-addrcl 7976
This theorem depends on definitions:  df-bi 117  df-cleq 2189  df-clel 2192  df-2 9049  df-3 9050  df-4 9051  df-5 9052  df-6 9053  df-7 9054
This theorem is referenced by:  7cn  9074  8re  9075  8pos  9093  5lt7  9176  4lt7  9177  3lt7  9178  2lt7  9179  1lt7  9180  7lt8  9181  6lt8  9182  7lt9  9189  6lt9  9190  7lt10  9589  6lt10  9590  lgsdir2lem1  15269
  Copyright terms: Public domain W3C validator