Theorem 8re 9077

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 9057	. 2 ⊢ 8 = (7 + 1)
2		7re 9075	. . 3 ⊢ 7 ∈ ℝ
3		1re 8027	. . 3 ⊢ 1 ∈ ℝ
4	2, 3	readdcli 8041	. 2 ⊢ (7 + 1) ∈ ℝ
5	1, 4	eqeltri 2269	1 ⊢ 8 ∈ ℝ

Syntax hints:   ∈ wcel 2167  (class class class)co 5923  ℝcr 7880  1c1 7882   + caddc 7884  7c7 9048  8c8 9049

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 1461  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-4 1524  ax-17 1540  ax-ial 1548  ax-ext 2178  ax-1re 7975  ax-addrcl 7978

This theorem depends on definitions:  df-bi 117  df-cleq 2189  df-clel 2192  df-2 9051  df-3 9052  df-4 9053  df-5 9054  df-6 9055  df-7 9056  df-8 9057

This theorem is referenced by:  8cn  9078  9re  9079  9pos  9096  6lt8  9184  5lt8  9185  4lt8  9186  3lt8  9187  2lt8  9188  1lt8  9189  8lt9  9190  7lt9  9191  8th4div3  9212  8lt10  9590  7lt10  9591  ef01bndlem  11923  cos2bnd  11927  slotstnscsi  12882  slotsdnscsi  12906  2lgsoddprmlem1  15356  2lgsoddprmlem2  15357  2lgsoddprmlem3a  15358  2lgsoddprmlem3b  15359  2lgsoddprmlem3c  15360  2lgsoddprmlem3d  15361