Theorem 8re 9392

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 9372	. 2 ⊢ 8 = (7 + 1)
2		7re 9390	. . 3 ⊢ 7 ∈ ℝ
3		1re 8326	. . 3 ⊢ 1 ∈ ℝ
4	2, 3	readdcli 8340	. 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 8179  1c1 8181   + caddc 8183  7c7 9363  8c8 9364

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 8274  ax-addrcl 8277

This proof depends on definitions:  df-bi 117  df-cleq 2231  df-clel 2234  df-2 9366  df-3 9367  df-4 9368  df-5 9369  df-6 9370  df-7 9371  df-8 9372

This theorem is used by:  8cn  9393  9re  9394  9pos  9411  6lt8  9501  5lt8  9502  4lt8  9503  3lt8  9504  2lt8  9505  1lt8  9506  8lt9  9507  7lt9  9508  8th4div3  9529  8lt10  9918  7lt10  9919  ef01bndlem  12542  cos2bnd  12546  slotstnscsi  13602  slotsdnscsi  13630  chtqub  16257  bposlem8  16279  bposlem9  16280  2lgsoddprmlem1  16390  2lgsoddprmlem2  16391  2lgsoddprmlem3a  16392  2lgsoddprmlem3b  16393  2lgsoddprmlem3c  16394  2lgsoddprmlem3d  16395