Theorem 8re 9339

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 9319	. 2 ⊢ 8 = (7 + 1)
2		7re 9337	. . 3 ⊢ 7 ∈ ℝ
3		1re 8289	. . 3 ⊢ 1 ∈ ℝ
4	2, 3	readdcli 8303	. 2 ⊢ (7 + 1) ∈ ℝ
5	1, 4	eqeltri 2307	1 ⊢ 8 ∈ ℝ

Syntax hints:   ∈ wcel 2205  (class class class)co 6058  ℝcr 8142  1c1 8144   + caddc 8146  7c7 9310  8c8 9311

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 1496  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-4 1559  ax-17 1575  ax-ial 1583  ax-ext 2216  ax-1re 8237  ax-addrcl 8240

This theorem depends on definitions:  df-bi 117  df-cleq 2227  df-clel 2230  df-2 9313  df-3 9314  df-4 9315  df-5 9316  df-6 9317  df-7 9318  df-8 9319

This theorem is referenced by:  8cn  9340  9re  9341  9pos  9358  6lt8  9446  5lt8  9447  4lt8  9448  3lt8  9449  2lt8  9450  1lt8  9451  8lt9  9452  7lt9  9453  8th4div3  9474  8lt10  9858  7lt10  9859  ef01bndlem  12467  cos2bnd  12471  slotstnscsi  13492  slotsdnscsi  13520  2lgsoddprmlem1  16104  2lgsoddprmlem2  16105  2lgsoddprmlem3a  16106  2lgsoddprmlem3b  16107  2lgsoddprmlem3c  16108  2lgsoddprmlem3d  16109