Theorem 8re 9121

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 9101	. 2 ⊢ 8 = (7 + 1)
2		7re 9119	. . 3 ⊢ 7 ∈ ℝ
3		1re 8071	. . 3 ⊢ 1 ∈ ℝ
4	2, 3	readdcli 8085	. 2 ⊢ (7 + 1) ∈ ℝ
5	1, 4	eqeltri 2278	1 ⊢ 8 ∈ ℝ

Syntax hints:   ∈ wcel 2176  (class class class)co 5944  ℝcr 7924  1c1 7926   + caddc 7928  7c7 9092  8c8 9093

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 1470  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-4 1533  ax-17 1549  ax-ial 1557  ax-ext 2187  ax-1re 8019  ax-addrcl 8022

This theorem depends on definitions:  df-bi 117  df-cleq 2198  df-clel 2201  df-2 9095  df-3 9096  df-4 9097  df-5 9098  df-6 9099  df-7 9100  df-8 9101

This theorem is referenced by:  8cn  9122  9re  9123  9pos  9140  6lt8  9228  5lt8  9229  4lt8  9230  3lt8  9231  2lt8  9232  1lt8  9233  8lt9  9234  7lt9  9235  8th4div3  9256  8lt10  9635  7lt10  9636  ef01bndlem  12067  cos2bnd  12071  slotstnscsi  13027  slotsdnscsi  13055  2lgsoddprmlem1  15582  2lgsoddprmlem2  15583  2lgsoddprmlem3a  15584  2lgsoddprmlem3b  15585  2lgsoddprmlem3c  15586  2lgsoddprmlem3d  15587