Theorem 8re 9195

Description: The number 8 is real. (Contributed by NM, 27-May-1999.)

Assertion

Ref	Expression
8re	|- 8 e. RR

Proof of Theorem 8re

Step	Hyp	Ref	Expression
1		df-8 9175	. 2 |- 8 = ( 7 + 1 )
2		7re 9193	. . 3 |- 7 e. RR
3		1re 8145	. . 3 |- 1 e. RR
4	2, 3	readdcli 8159	. 2 |- ( 7 + 1 ) e. RR
5	1, 4	eqeltri 2302	1 |- 8 e. RR

Syntax hints:   e. wcel 2200  (class class class)co 6001   RRcr 7998   1c1 8000   + caddc 8002   7c7 9166   8c8 9167

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  df-7 9174  df-8 9175

This theorem is referenced by:  8cn  9196  9re  9197  9pos  9214  6lt8  9302  5lt8  9303  4lt8  9304  3lt8  9305  2lt8  9306  1lt8  9307  8lt9  9308  7lt9  9309  8th4div3  9330  8lt10  9709  7lt10  9710  ef01bndlem  12267  cos2bnd  12271  slotstnscsi  13228  slotsdnscsi  13256  2lgsoddprmlem1  15784  2lgsoddprmlem2  15785  2lgsoddprmlem3a  15786  2lgsoddprmlem3b  15787  2lgsoddprmlem3c  15788  2lgsoddprmlem3d  15789