Theorem 7re 9193

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 9174	. 2 |- 7 = ( 6 + 1 )
2		6re 9191	. . 3 |- 6 e. RR
3		1re 8145	. . 3 |- 1 e. RR
4	2, 3	readdcli 8159	. 2 |- ( 6 + 1 ) e. RR
5	1, 4	eqeltri 2302	1 |- 7 e. RR

Syntax hints:   e. wcel 2200  (class class class)co 6001   RRcr 7998   1c1 8000   + caddc 8002   6c6 9165   7c7 9166

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 1493  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-4 1556  ax-17 1572  ax-ial 1580  ax-ext 2211  ax-1re 8093  ax-addrcl 8096

This theorem depends on definitions:  df-bi 117  df-cleq 2222  df-clel 2225  df-2 9169  df-3 9170  df-4 9171  df-5 9172  df-6 9173  df-7 9174

This theorem is referenced by:  7cn  9194  8re  9195  8pos  9213  5lt7  9296  4lt7  9297  3lt7  9298  2lt7  9299  1lt7  9300  7lt8  9301  6lt8  9302  7lt9  9309  6lt9  9310  7lt10  9710  6lt10  9711  lgsdir2lem1  15707