Theorem 7re 8940

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 8921	. 2 |- 7 = ( 6 + 1 )
2		6re 8938	. . 3 |- 6 e. RR
3		1re 7898	. . 3 |- 1 e. RR
4	2, 3	readdcli 7912	. 2 |- ( 6 + 1 ) e. RR
5	1, 4	eqeltri 2239	1 |- 7 e. RR

Syntax hints:   e. wcel 2136  (class class class)co 5842   RRcr 7752   1c1 7754   + caddc 7756   6c6 8912   7c7 8913

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1435  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-4 1498  ax-17 1514  ax-ial 1522  ax-ext 2147  ax-1re 7847  ax-addrcl 7850

This theorem depends on definitions:  df-bi 116  df-cleq 2158  df-clel 2161  df-2 8916  df-3 8917  df-4 8918  df-5 8919  df-6 8920  df-7 8921

This theorem is referenced by:  7cn  8941  8re  8942  8pos  8960  5lt7  9042  4lt7  9043  3lt7  9044  2lt7  9045  1lt7  9046  7lt8  9047  6lt8  9048  7lt9  9055  6lt9  9056  7lt10  9454  6lt10  9455  lgsdir2lem1  13569