Theorem 8re 9398

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 9378	. 2 |- 8 = ( 7 + 1 )
2		7re 9396	. . 3 |- 7 e. RR
3		1re 8331	. . 3 |- 1 e. RR
4	2, 3	readdcli 8345	. 2 |- ( 7 + 1 ) e. RR
5	1, 4	eqeltri 2311	1 |- 8 e. RR

This proof depends on syntax axioms:   e. wcel 2209  (class class class)co 6088   RRcr 8184   1c1 8186   + caddc 8188   7c7 9369   8c8 9370

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1500  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-4 1563  ax-17 1579  ax-ial 1587  ax-ext 2220  ax-1re 8279  ax-addrcl 8282

This proof depends on definitions:  df-bi 117  df-cleq 2231  df-clel 2234  df-2 9372  df-3 9373  df-4 9374  df-5 9375  df-6 9376  df-7 9377  df-8 9378

This theorem is used by:  8cn  9399  9re  9400  9pos  9417  6lt8  9507  5lt8  9508  4lt8  9509  3lt8  9510  2lt8  9511  1lt8  9512  8lt9  9513  7lt9  9514  8th4div3  9535  8lt10  9924  7lt10  9925  ef01bndlem  12548  cos2bnd  12552  slotstnscsi  13608  slotsdnscsi  13636  chtqub  16296  bposlem8  16318  bposlem9  16319  2lgsoddprmlem1  16429  2lgsoddprmlem2  16430  2lgsoddprmlem3a  16431  2lgsoddprmlem3b  16432  2lgsoddprmlem3c  16433  2lgsoddprmlem3d  16434