Theorem 8re 9368

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 9348	. 2 ⊢ 8 = (7 + 1)
2		7re 9366	. . 3 ⊢ 7 ∈ ℝ
3		1re 8315	. . 3 ⊢ 1 ∈ ℝ
4	2, 3	readdcli 8329	. 2 ⊢ (7 + 1) ∈ ℝ
5	1, 4	eqeltri 2311	1 ⊢ 8 ∈ ℝ

Syntax hints:   ∈ wcel 2209  (class class class)co 6075  ℝcr 8168  1c1 8170   + caddc 8172  7c7 9339  8c8 9340

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 1500  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-4 1563  ax-17 1579  ax-ial 1587  ax-ext 2220  ax-1re 8263  ax-addrcl 8266

This theorem depends on definitions:  df-bi 117  df-cleq 2231  df-clel 2234  df-2 9342  df-3 9343  df-4 9344  df-5 9345  df-6 9346  df-7 9347  df-8 9348

This theorem is referenced by:  8cn  9369  9re  9370  9pos  9387  6lt8  9475  5lt8  9476  4lt8  9477  3lt8  9478  2lt8  9479  1lt8  9480  8lt9  9481  7lt9  9482  8th4div3  9503  8lt10  9887  7lt10  9888  ef01bndlem  12501  cos2bnd  12505  slotstnscsi  13526  slotsdnscsi  13554  2lgsoddprmlem1  16138  2lgsoddprmlem2  16139  2lgsoddprmlem3a  16140  2lgsoddprmlem3b  16141  2lgsoddprmlem3c  16142  2lgsoddprmlem3d  16143