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Theorem 7re 8073
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 8054 . 2  |-  7  =  ( 6  +  1 )
2 6re 8071 . . 3  |-  6  e.  RR
3 1re 7084 . . 3  |-  1  e.  RR
42, 3readdcli 7098 . 2  |-  ( 6  +  1 )  e.  RR
51, 4eqeltri 2126 1  |-  7  e.  RR
Colors of variables: wff set class
Syntax hints:    e. wcel 1409  (class class class)co 5540   RRcr 6946   1c1 6948    + caddc 6950   6c6 8044   7c7 8045
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-4 1416  ax-17 1435  ax-ial 1443  ax-ext 2038  ax-1re 7036  ax-addrcl 7039
This theorem depends on definitions:  df-bi 114  df-cleq 2049  df-clel 2052  df-2 8049  df-3 8050  df-4 8051  df-5 8052  df-6 8053  df-7 8054
This theorem is referenced by:  7cn  8074  8re  8075  8pos  8093  5lt7  8168  4lt7  8169  3lt7  8170  2lt7  8171  1lt7  8172  7lt8  8173  6lt8  8174  7lt9  8181  6lt9  8182  7lt10  8559  6lt10  8560
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