Theorem 8re 9206

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

Assertion

Ref	Expression
8re	⊢ 8 ∈ ℝ

Proof of Theorem 8re

Step	Hyp	Ref	Expression
1		df-8 9186	. 2 ⊢ 8 = (7 + 1)
2		7re 9204	. . 3 ⊢ 7 ∈ ℝ
3		1re 8156	. . 3 ⊢ 1 ∈ ℝ
4	2, 3	readdcli 8170	. 2 ⊢ (7 + 1) ∈ ℝ
5	1, 4	eqeltri 2302	1 ⊢ 8 ∈ ℝ

Syntax hints:   ∈ wcel 2200  (class class class)co 6007  ℝcr 8009  1c1 8011   + caddc 8013  7c7 9177  8c8 9178

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  df-7 9185  df-8 9186

This theorem is referenced by:  8cn  9207  9re  9208  9pos  9225  6lt8  9313  5lt8  9314  4lt8  9315  3lt8  9316  2lt8  9317  1lt8  9318  8lt9  9319  7lt9  9320  8th4div3  9341  8lt10  9720  7lt10  9721  ef01bndlem  12282  cos2bnd  12286  slotstnscsi  13243  slotsdnscsi  13271  2lgsoddprmlem1  15799  2lgsoddprmlem2  15800  2lgsoddprmlem3a  15801  2lgsoddprmlem3b  15802  2lgsoddprmlem3c  15803  2lgsoddprmlem3d  15804