Theorem 7re 9285

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 9266	. 2 |- 7 = ( 6 + 1 )
2		6re 9283	. . 3 |- 6 e. RR
3		1re 8238	. . 3 |- 1 e. RR
4	2, 3	readdcli 8252	. 2 |- ( 6 + 1 ) e. RR
5	1, 4	eqeltri 2304	1 |- 7 e. RR

Syntax hints:   e. wcel 2202  (class class class)co 6028   RRcr 8091   1c1 8093   + caddc 8095   6c6 9257   7c7 9258

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 1496  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-4 1559  ax-17 1575  ax-ial 1583  ax-ext 2213  ax-1re 8186  ax-addrcl 8189

This theorem depends on definitions:  df-bi 117  df-cleq 2224  df-clel 2227  df-2 9261  df-3 9262  df-4 9263  df-5 9264  df-6 9265  df-7 9266

This theorem is referenced by:  7cn  9286  8re  9287  8pos  9305  5lt7  9388  4lt7  9389  3lt7  9390  2lt7  9391  1lt7  9392  7lt8  9393  6lt8  9394  7lt9  9401  6lt9  9402  7lt10  9804  6lt10  9805  lgsdir2lem1  15847