Theorem 9re 9069

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

Assertion

Ref	Expression
9re	|- 9 e. RR

Proof of Theorem 9re

Step	Hyp	Ref	Expression
1		df-9 9048	. 2 |- 9 = ( 8 + 1 )
2		8re 9067	. . 3 |- 8 e. RR
3		1re 8018	. . 3 |- 1 e. RR
4	2, 3	readdcli 8032	. 2 |- ( 8 + 1 ) e. RR
5	1, 4	eqeltri 2266	1 |- 9 e. RR

Syntax hints:   e. wcel 2164  (class class class)co 5918   RRcr 7871   1c1 7873   + caddc 7875   8c8 9039   9c9 9040

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 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-17 1537  ax-ial 1545  ax-ext 2175  ax-1re 7966  ax-addrcl 7969

This theorem depends on definitions:  df-bi 117  df-cleq 2186  df-clel 2189  df-2 9041  df-3 9042  df-4 9043  df-5 9044  df-6 9045  df-7 9046  df-8 9047  df-9 9048

This theorem is referenced by:  9cn  9070  7lt9  9180  6lt9  9181  5lt9  9182  4lt9  9183  3lt9  9184  2lt9  9185  1lt9  9186  9lt10  9578  8lt10  9579  0.999...  11664  cos2bnd  11903  sincos2sgn  11909  slotsdifplendx  12827  dsndxntsetndx  12837  unifndxntsetndx  12844  cnfldstr  14049  setsmsdsg  14648  2logb9irr  15103  2logb9irrap  15109