Theorem 6re 8120

Description: The number 6 is real. (Contributed by NM, 27-May-1999.)

Assertion

Ref	Expression
6re	|- 6 e. RR

Proof of Theorem 6re

Step	Hyp	Ref	Expression
1		df-6 8102	. 2 |- 6 = ( 5 + 1 )
2		5re 8118	. . 3 |- 5 e. RR
3		1re 7118	. . 3 |- 1 e. RR
4	2, 3	readdcli 7132	. 2 |- ( 5 + 1 ) e. RR
5	1, 4	eqeltri 2151	1 |- 6 e. RR

Syntax hints:   e. wcel 1433  (class class class)co 5532   RRcr 6980   1c1 6982   + caddc 6984   5c5 8092   6c6 8093

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  df-6 8102

This theorem is referenced by:  6cn  8121  7re  8122  7pos  8141  4lt6  8212  3lt6  8213  2lt6  8214  1lt6  8215  6lt7  8216  5lt7  8217  6lt8  8223  5lt8  8224  6lt9  8231  5lt9  8232  8th4div3  8250  halfpm6th  8251  div4p1lem1div2  8284  6lt10  8610  5lt10  8611