Theorem 8re 9191

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 9171	. 2 ⊢ 8 = (7 + 1)
2		7re 9189	. . 3 ⊢ 7 ∈ ℝ
3		1re 8141	. . 3 ⊢ 1 ∈ ℝ
4	2, 3	readdcli 8155	. 2 ⊢ (7 + 1) ∈ ℝ
5	1, 4	eqeltri 2302	1 ⊢ 8 ∈ ℝ

Syntax hints:   ∈ wcel 2200  (class class class)co 6000  ℝcr 7994  1c1 7996   + caddc 7998  7c7 9162  8c8 9163

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 8089  ax-addrcl 8092

This theorem depends on definitions:  df-bi 117  df-cleq 2222  df-clel 2225  df-2 9165  df-3 9166  df-4 9167  df-5 9168  df-6 9169  df-7 9170  df-8 9171

This theorem is referenced by:  8cn  9192  9re  9193  9pos  9210  6lt8  9298  5lt8  9299  4lt8  9300  3lt8  9301  2lt8  9302  1lt8  9303  8lt9  9304  7lt9  9305  8th4div3  9326  8lt10  9705  7lt10  9706  ef01bndlem  12262  cos2bnd  12266  slotstnscsi  13223  slotsdnscsi  13251  2lgsoddprmlem1  15778  2lgsoddprmlem2  15779  2lgsoddprmlem3a  15780  2lgsoddprmlem3b  15781  2lgsoddprmlem3c  15782  2lgsoddprmlem3d  15783