Theorem 8re 9094

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 9074	. 2 ⊢ 8 = (7 + 1)
2		7re 9092	. . 3 ⊢ 7 ∈ ℝ
3		1re 8044	. . 3 ⊢ 1 ∈ ℝ
4	2, 3	readdcli 8058	. 2 ⊢ (7 + 1) ∈ ℝ
5	1, 4	eqeltri 2269	1 ⊢ 8 ∈ ℝ

Syntax hints:   ∈ wcel 2167  (class class class)co 5925  ℝcr 7897  1c1 7899   + caddc 7901  7c7 9065  8c8 9066

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 7992  ax-addrcl 7995

This theorem depends on definitions:  df-bi 117  df-cleq 2189  df-clel 2192  df-2 9068  df-3 9069  df-4 9070  df-5 9071  df-6 9072  df-7 9073  df-8 9074

This theorem is referenced by:  8cn  9095  9re  9096  9pos  9113  6lt8  9201  5lt8  9202  4lt8  9203  3lt8  9204  2lt8  9205  1lt8  9206  8lt9  9207  7lt9  9208  8th4div3  9229  8lt10  9607  7lt10  9608  ef01bndlem  11940  cos2bnd  11944  slotstnscsi  12899  slotsdnscsi  12927  2lgsoddprmlem1  15454  2lgsoddprmlem2  15455  2lgsoddprmlem3a  15456  2lgsoddprmlem3b  15457  2lgsoddprmlem3c  15458  2lgsoddprmlem3d  15459