Theorem 8re 9156

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 9136	. 2 ⊢ 8 = (7 + 1)
2		7re 9154	. . 3 ⊢ 7 ∈ ℝ
3		1re 8106	. . 3 ⊢ 1 ∈ ℝ
4	2, 3	readdcli 8120	. 2 ⊢ (7 + 1) ∈ ℝ
5	1, 4	eqeltri 2280	1 ⊢ 8 ∈ ℝ

Syntax hints:   ∈ wcel 2178  (class class class)co 5967  ℝcr 7959  1c1 7961   + caddc 7963  7c7 9127  8c8 9128

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 1471  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-4 1534  ax-17 1550  ax-ial 1558  ax-ext 2189  ax-1re 8054  ax-addrcl 8057

This theorem depends on definitions:  df-bi 117  df-cleq 2200  df-clel 2203  df-2 9130  df-3 9131  df-4 9132  df-5 9133  df-6 9134  df-7 9135  df-8 9136

This theorem is referenced by:  8cn  9157  9re  9158  9pos  9175  6lt8  9263  5lt8  9264  4lt8  9265  3lt8  9266  2lt8  9267  1lt8  9268  8lt9  9269  7lt9  9270  8th4div3  9291  8lt10  9670  7lt10  9671  ef01bndlem  12182  cos2bnd  12186  slotstnscsi  13142  slotsdnscsi  13170  2lgsoddprmlem1  15697  2lgsoddprmlem2  15698  2lgsoddprmlem3a  15699  2lgsoddprmlem3b  15700  2lgsoddprmlem3c  15701  2lgsoddprmlem3d  15702