Theorem 7re 9005

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 8986	. 2 |- 7 = ( 6 + 1 )
2		6re 9003	. . 3 |- 6 e. RR
3		1re 7959	. . 3 |- 1 e. RR
4	2, 3	readdcli 7973	. 2 |- ( 6 + 1 ) e. RR
5	1, 4	eqeltri 2250	1 |- 7 e. RR

Syntax hints:   e. wcel 2148  (class class class)co 5878   RRcr 7813   1c1 7815   + caddc 7817   6c6 8977   7c7 8978

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 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-17 1526  ax-ial 1534  ax-ext 2159  ax-1re 7908  ax-addrcl 7911

This theorem depends on definitions:  df-bi 117  df-cleq 2170  df-clel 2173  df-2 8981  df-3 8982  df-4 8983  df-5 8984  df-6 8985  df-7 8986

This theorem is referenced by:  7cn  9006  8re  9007  8pos  9025  5lt7  9107  4lt7  9108  3lt7  9109  2lt7  9110  1lt7  9111  7lt8  9112  6lt8  9113  7lt9  9120  6lt9  9121  7lt10  9519  6lt10  9520  lgsdir2lem1  14617