Theorem 8re 9067

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 9047	. 2 ⊢ 8 = (7 + 1)
2		7re 9065	. . 3 ⊢ 7 ∈ ℝ
3		1re 8018	. . 3 ⊢ 1 ∈ ℝ
4	2, 3	readdcli 8032	. 2 ⊢ (7 + 1) ∈ ℝ
5	1, 4	eqeltri 2266	1 ⊢ 8 ∈ ℝ

Syntax hints:   ∈ wcel 2164  (class class class)co 5918  ℝcr 7871  1c1 7873   + caddc 7875  7c7 9038  8c8 9039

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 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-17 1537  ax-ial 1545  ax-ext 2175  ax-1re 7966  ax-addrcl 7969

This theorem depends on definitions:  df-bi 117  df-cleq 2186  df-clel 2189  df-2 9041  df-3 9042  df-4 9043  df-5 9044  df-6 9045  df-7 9046  df-8 9047

This theorem is referenced by:  8cn  9068  9re  9069  9pos  9086  6lt8  9173  5lt8  9174  4lt8  9175  3lt8  9176  2lt8  9177  1lt8  9178  8lt9  9179  7lt9  9180  8th4div3  9201  8lt10  9579  7lt10  9580  ef01bndlem  11899  cos2bnd  11903  slotstnscsi  12812  slotsdnscsi  12836  2lgsoddprmlem1  15193  2lgsoddprmlem2  15194  2lgsoddprmlem3a  15195  2lgsoddprmlem3b  15196  2lgsoddprmlem3c  15197  2lgsoddprmlem3d  15198