Theorem 5re 8118

Description: The number 5 is real. (Contributed by NM, 27-May-1999.)

Assertion

Ref	Expression
5re	|- 5 e. RR

Proof of Theorem 5re

Step	Hyp	Ref	Expression
1		df-5 8101	. 2 |- 5 = ( 4 + 1 )
2		4re 8116	. . 3 |- 4 e. RR
3		1re 7118	. . 3 |- 1 e. RR
4	2, 3	readdcli 7132	. 2 |- ( 4 + 1 ) e. RR
5	1, 4	eqeltri 2151	1 |- 5 e. RR

Syntax hints:   e. wcel 1433  (class class class)co 5532   RRcr 6980   1c1 6982   + caddc 6984   4c4 8091   5c5 8092

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-4 1440  ax-17 1459  ax-ial 1467  ax-ext 2063  ax-1re 7070  ax-addrcl 7073

This theorem depends on definitions:  df-bi 115  df-cleq 2074  df-clel 2077  df-2 8098  df-3 8099  df-4 8100  df-5 8101

This theorem is referenced by:  5cn  8119  6re  8120  6pos  8140  3lt5  8208  2lt5  8209  1lt5  8210  5lt6  8211  4lt6  8212  5lt7  8217  4lt7  8218  5lt8  8224  4lt8  8225  5lt9  8232  4lt9  8233  5lt10  8611  4lt10  8612