Theorem 9re 9071

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 9050	. 2 |- 9 = ( 8 + 1 )
2		8re 9069	. . 3 |- 8 e. RR
3		1re 8020	. . 3 |- 1 e. RR
4	2, 3	readdcli 8034	. 2 |- ( 8 + 1 ) e. RR
5	1, 4	eqeltri 2266	1 |- 9 e. RR

Syntax hints:   e. wcel 2164  (class class class)co 5919   RRcr 7873   1c1 7875   + caddc 7877   8c8 9041   9c9 9042

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 7968  ax-addrcl 7971

This theorem depends on definitions:  df-bi 117  df-cleq 2186  df-clel 2189  df-2 9043  df-3 9044  df-4 9045  df-5 9046  df-6 9047  df-7 9048  df-8 9049  df-9 9050

This theorem is referenced by:  9cn  9072  7lt9  9183  6lt9  9184  5lt9  9185  4lt9  9186  3lt9  9187  2lt9  9188  1lt9  9189  9lt10  9581  8lt10  9582  0.999...  11667  cos2bnd  11906  sincos2sgn  11912  slotsdifplendx  12830  dsndxntsetndx  12840  unifndxntsetndx  12847  setsmsdsg  14659  2logb9irr  15144  2logb9irrap  15150