Theorem 9re 9341

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 9320	. 2 |- 9 = ( 8 + 1 )
2		8re 9339	. . 3 |- 8 e. RR
3		1re 8289	. . 3 |- 1 e. RR
4	2, 3	readdcli 8303	. 2 |- ( 8 + 1 ) e. RR
5	1, 4	eqeltri 2307	1 |- 9 e. RR

Syntax hints:   e. wcel 2205  (class class class)co 6058   RRcr 8142   1c1 8144   + caddc 8146   8c8 9311   9c9 9312

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 1496  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-4 1559  ax-17 1575  ax-ial 1583  ax-ext 2216  ax-1re 8237  ax-addrcl 8240

This theorem depends on definitions:  df-bi 117  df-cleq 2227  df-clel 2230  df-2 9313  df-3 9314  df-4 9315  df-5 9316  df-6 9317  df-7 9318  df-8 9319  df-9 9320

This theorem is referenced by:  9cn  9342  7lt9  9453  6lt9  9454  5lt9  9455  4lt9  9456  3lt9  9457  2lt9  9458  1lt9  9459  9lt10  9857  8lt10  9858  0.999...  12232  cos2bnd  12471  sincos2sgn  12477  slotsdifplendx  13507  dsndxntsetndx  13521  unifndxntsetndx  13528  setsmsdsg  15471  2logb9irr  15962  2logb9irrap  15968