Theorem 7re 9065

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 9046	. 2 |- 7 = ( 6 + 1 )
2		6re 9063	. . 3 |- 6 e. RR
3		1re 8018	. . 3 |- 1 e. RR
4	2, 3	readdcli 8032	. 2 |- ( 6 + 1 ) e. RR
5	1, 4	eqeltri 2266	1 |- 7 e. RR

Syntax hints:   e. wcel 2164  (class class class)co 5918   RRcr 7871   1c1 7873   + caddc 7875   6c6 9037   7c7 9038

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 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-17 1537  ax-ial 1545  ax-ext 2175  ax-1re 7966  ax-addrcl 7969

This theorem depends on definitions:  df-bi 117  df-cleq 2186  df-clel 2189  df-2 9041  df-3 9042  df-4 9043  df-5 9044  df-6 9045  df-7 9046

This theorem is referenced by:  7cn  9066  8re  9067  8pos  9085  5lt7  9167  4lt7  9168  3lt7  9169  2lt7  9170  1lt7  9171  7lt8  9172  6lt8  9173  7lt9  9180  6lt9  9181  7lt10  9580  6lt10  9581  lgsdir2lem1  15144