Theorem 6re 9202

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 9184	. 2 |- 6 = ( 5 + 1 )
2		5re 9200	. . 3 |- 5 e. RR
3		1re 8156	. . 3 |- 1 e. RR
4	2, 3	readdcli 8170	. 2 |- ( 5 + 1 ) e. RR
5	1, 4	eqeltri 2302	1 |- 6 e. RR

Syntax hints:   e. wcel 2200  (class class class)co 6007   RRcr 8009   1c1 8011   + caddc 8013   5c5 9175   6c6 9176

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 1493  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-4 1556  ax-17 1572  ax-ial 1580  ax-ext 2211  ax-1re 8104  ax-addrcl 8107

This theorem depends on definitions:  df-bi 117  df-cleq 2222  df-clel 2225  df-2 9180  df-3 9181  df-4 9182  df-5 9183  df-6 9184

This theorem is referenced by:  6cn  9203  7re  9204  7pos  9223  4lt6  9302  3lt6  9303  2lt6  9304  1lt6  9305  6lt7  9306  5lt7  9307  6lt8  9313  5lt8  9314  6lt9  9321  5lt9  9322  8th4div3  9341  halfpm6th  9342  div4p1lem1div2  9376  6lt10  9722  5lt10  9723  5recm6rec  9732  efi4p  12244  resin4p  12245  recos4p  12246  ef01bndlem  12283  sin01bnd  12284  cos01bnd  12285  slotsdifipndx  13224  slotstnscsi  13244  plendxnvscandx  13258  slotsdnscsi  13272  sincos6thpi  15532  pigt3  15534