Theorem 9re 9094

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 9073	. 2 |- 9 = ( 8 + 1 )
2		8re 9092	. . 3 |- 8 e. RR
3		1re 8042	. . 3 |- 1 e. RR
4	2, 3	readdcli 8056	. 2 |- ( 8 + 1 ) e. RR
5	1, 4	eqeltri 2269	1 |- 9 e. RR

Syntax hints:   e. wcel 2167  (class class class)co 5925   RRcr 7895   1c1 7897   + caddc 7899   8c8 9064   9c9 9065

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 7990  ax-addrcl 7993

This theorem depends on definitions:  df-bi 117  df-cleq 2189  df-clel 2192  df-2 9066  df-3 9067  df-4 9068  df-5 9069  df-6 9070  df-7 9071  df-8 9072  df-9 9073

This theorem is referenced by:  9cn  9095  7lt9  9206  6lt9  9207  5lt9  9208  4lt9  9209  3lt9  9210  2lt9  9211  1lt9  9212  9lt10  9604  8lt10  9605  0.999...  11703  cos2bnd  11942  sincos2sgn  11948  slotsdifplendx  12912  dsndxntsetndx  12926  unifndxntsetndx  12933  setsmsdsg  14800  2logb9irr  15291  2logb9irrap  15297