Theorem 9re 8126

Description: The number 9 is real. (Contributed by NM, 27-May-1999.)

Assertion

Ref	Expression
9re	⊢ 9 ∈ ℝ

Proof of Theorem 9re

Step	Hyp	Ref	Expression
1		df-9 8105	. 2 ⊢ 9 = (8 + 1)
2		8re 8124	. . 3 ⊢ 8 ∈ ℝ
3		1re 7118	. . 3 ⊢ 1 ∈ ℝ
4	2, 3	readdcli 7132	. 2 ⊢ (8 + 1) ∈ ℝ
5	1, 4	eqeltri 2151	1 ⊢ 9 ∈ ℝ

Syntax hints:   ∈ wcel 1433  (class class class)co 5532  ℝcr 6980  1c1 6982   + caddc 6984  8c8 8095  9c9 8096

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-4 1440  ax-17 1459  ax-ial 1467  ax-ext 2063  ax-1re 7070  ax-addrcl 7073

This theorem depends on definitions:  df-bi 115  df-cleq 2074  df-clel 2077  df-2 8098  df-3 8099  df-4 8100  df-5 8101  df-6 8102  df-7 8103  df-8 8104  df-9 8105

This theorem is referenced by:  9cn  8127  7lt9  8230  6lt9  8231  5lt9  8232  4lt9  8233  3lt9  8234  2lt9  8235  1lt9  8236  9lt10  8607  8lt10  8608