Theorem 7re 9231

Description: The number 7 is real. (Contributed by NM, 27-May-1999.)

Assertion

Ref	Expression
7re	|- 7 e. RR

Proof of Theorem 7re

Step	Hyp	Ref	Expression
1		df-7 9212	. 2 |- 7 = ( 6 + 1 )
2		6re 9229	. . 3 |- 6 e. RR
3		1re 8183	. . 3 |- 1 e. RR
4	2, 3	readdcli 8197	. 2 |- ( 6 + 1 ) e. RR
5	1, 4	eqeltri 2303	1 |- 7 e. RR

Syntax hints:   e. wcel 2201  (class class class)co 6023   RRcr 8036   1c1 8038   + caddc 8040   6c6 9203   7c7 9204

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 1495  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-4 1558  ax-17 1574  ax-ial 1582  ax-ext 2212  ax-1re 8131  ax-addrcl 8134

This theorem depends on definitions:  df-bi 117  df-cleq 2223  df-clel 2226  df-2 9207  df-3 9208  df-4 9209  df-5 9210  df-6 9211  df-7 9212

This theorem is referenced by:  7cn  9232  8re  9233  8pos  9251  5lt7  9334  4lt7  9335  3lt7  9336  2lt7  9337  1lt7  9338  7lt8  9339  6lt8  9340  7lt9  9347  6lt9  9348  7lt10  9748  6lt10  9749  lgsdir2lem1  15786