Theorem 6re 9191

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 9173	. 2 |- 6 = ( 5 + 1 )
2		5re 9189	. . 3 |- 5 e. RR
3		1re 8145	. . 3 |- 1 e. RR
4	2, 3	readdcli 8159	. 2 |- ( 5 + 1 ) e. RR
5	1, 4	eqeltri 2302	1 |- 6 e. RR

Syntax hints:   e. wcel 2200  (class class class)co 6001   RRcr 7998   1c1 8000   + caddc 8002   5c5 9164   6c6 9165

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 8093  ax-addrcl 8096

This theorem depends on definitions:  df-bi 117  df-cleq 2222  df-clel 2225  df-2 9169  df-3 9170  df-4 9171  df-5 9172  df-6 9173

This theorem is referenced by:  6cn  9192  7re  9193  7pos  9212  4lt6  9291  3lt6  9292  2lt6  9293  1lt6  9294  6lt7  9295  5lt7  9296  6lt8  9302  5lt8  9303  6lt9  9310  5lt9  9311  8th4div3  9330  halfpm6th  9331  div4p1lem1div2  9365  6lt10  9711  5lt10  9712  5recm6rec  9721  efi4p  12228  resin4p  12229  recos4p  12230  ef01bndlem  12267  sin01bnd  12268  cos01bnd  12269  slotsdifipndx  13208  slotstnscsi  13228  plendxnvscandx  13242  slotsdnscsi  13256  sincos6thpi  15516  pigt3  15518