Theorem 8re 9391

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 9371	. 2 ⊢ 8 = (7 + 1)
2		7re 9389	. . 3 ⊢ 7 ∈ ℝ
3		1re 8325	. . 3 ⊢ 1 ∈ ℝ
4	2, 3	readdcli 8339	. 2 ⊢ (7 + 1) ∈ ℝ
5	1, 4	eqeltri 2311	1 ⊢ 8 ∈ ℝ

This proof depends on syntax axioms:   ∈ wcel 2209  (class class class)co 6085  ℝcr 8178  1c1 8180   + caddc 8182  7c7 9362  8c8 9363

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 8273  ax-addrcl 8276

This proof depends on definitions:  df-bi 117  df-cleq 2231  df-clel 2234  df-2 9365  df-3 9366  df-4 9367  df-5 9368  df-6 9369  df-7 9370  df-8 9371

This theorem is used by:  8cn  9392  9re  9393  9pos  9410  6lt8  9500  5lt8  9501  4lt8  9502  3lt8  9503  2lt8  9504  1lt8  9505  8lt9  9506  7lt9  9507  8th4div3  9528  8lt10  9917  7lt10  9918  ef01bndlem  12539  cos2bnd  12543  slotstnscsi  13598  slotsdnscsi  13626  2lgsoddprmlem1  16322  2lgsoddprmlem2  16323  2lgsoddprmlem3a  16324  2lgsoddprmlem3b  16325  2lgsoddprmlem3c  16326  2lgsoddprmlem3d  16327