Theorem 8re 9075

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 9055	. 2 |- 8 = ( 7 + 1 )
2		7re 9073	. . 3 |- 7 e. RR
3		1re 8025	. . 3 |- 1 e. RR
4	2, 3	readdcli 8039	. 2 |- ( 7 + 1 ) e. RR
5	1, 4	eqeltri 2269	1 |- 8 e. RR

Syntax hints:   e. wcel 2167  (class class class)co 5922   RRcr 7878   1c1 7880   + caddc 7882   7c7 9046   8c8 9047

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 1461  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-4 1524  ax-17 1540  ax-ial 1548  ax-ext 2178  ax-1re 7973  ax-addrcl 7976

This theorem depends on definitions:  df-bi 117  df-cleq 2189  df-clel 2192  df-2 9049  df-3 9050  df-4 9051  df-5 9052  df-6 9053  df-7 9054  df-8 9055

This theorem is referenced by:  8cn  9076  9re  9077  9pos  9094  6lt8  9182  5lt8  9183  4lt8  9184  3lt8  9185  2lt8  9186  1lt8  9187  8lt9  9188  7lt9  9189  8th4div3  9210  8lt10  9588  7lt10  9589  ef01bndlem  11921  cos2bnd  11925  slotstnscsi  12872  slotsdnscsi  12896  2lgsoddprmlem1  15346  2lgsoddprmlem2  15347  2lgsoddprmlem3a  15348  2lgsoddprmlem3b  15349  2lgsoddprmlem3c  15350  2lgsoddprmlem3d  15351