Theorem 7re 8603

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 8584	. 2 |- 7 = ( 6 + 1 )
2		6re 8601	. . 3 |- 6 e. RR
3		1re 7584	. . 3 |- 1 e. RR
4	2, 3	readdcli 7598	. 2 |- ( 6 + 1 ) e. RR
5	1, 4	eqeltri 2167	1 |- 7 e. RR

Syntax hints:   e. wcel 1445  (class class class)co 5690   RRcr 7446   1c1 7448   + caddc 7450   6c6 8575   7c7 8576

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1388  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-4 1452  ax-17 1471  ax-ial 1479  ax-ext 2077  ax-1re 7536  ax-addrcl 7539

This theorem depends on definitions:  df-bi 116  df-cleq 2088  df-clel 2091  df-2 8579  df-3 8580  df-4 8581  df-5 8582  df-6 8583  df-7 8584

This theorem is referenced by:  7cn  8604  8re  8605  8pos  8623  5lt7  8699  4lt7  8700  3lt7  8701  2lt7  8702  1lt7  8703  7lt8  8704  6lt8  8705  7lt9  8712  6lt9  8713  7lt10  9108  6lt10  9109