Theorem 7re 8796

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 8777	. 2 |- 7 = ( 6 + 1 )
2		6re 8794	. . 3 |- 6 e. RR
3		1re 7758	. . 3 |- 1 e. RR
4	2, 3	readdcli 7772	. 2 |- ( 6 + 1 ) e. RR
5	1, 4	eqeltri 2210	1 |- 7 e. RR

Syntax hints:   e. wcel 1480  (class class class)co 5767   RRcr 7612   1c1 7614   + caddc 7616   6c6 8768   7c7 8769

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 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-17 1506  ax-ial 1514  ax-ext 2119  ax-1re 7707  ax-addrcl 7710

This theorem depends on definitions:  df-bi 116  df-cleq 2130  df-clel 2133  df-2 8772  df-3 8773  df-4 8774  df-5 8775  df-6 8776  df-7 8777

This theorem is referenced by:  7cn  8797  8re  8798  8pos  8816  5lt7  8898  4lt7  8899  3lt7  8900  2lt7  8901  1lt7  8902  7lt8  8903  6lt8  8904  7lt9  8911  6lt9  8912  7lt10  9307  6lt10  9308