Theorem 9re 9077

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 9056	. 2 |- 9 = ( 8 + 1 )
2		8re 9075	. . 3 |- 8 e. RR
3		1re 8025	. . 3 |- 1 e. RR
4	2, 3	readdcli 8039	. 2 |- ( 8 + 1 ) e. RR
5	1, 4	eqeltri 2269	1 |- 9 e. RR

Syntax hints:   e. wcel 2167  (class class class)co 5922   RRcr 7878   1c1 7880   + caddc 7882   8c8 9047   9c9 9048

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 7973  ax-addrcl 7976

This theorem depends on definitions:  df-bi 117  df-cleq 2189  df-clel 2192  df-2 9049  df-3 9050  df-4 9051  df-5 9052  df-6 9053  df-7 9054  df-8 9055  df-9 9056

This theorem is referenced by:  9cn  9078  7lt9  9189  6lt9  9190  5lt9  9191  4lt9  9192  3lt9  9193  2lt9  9194  1lt9  9195  9lt10  9587  8lt10  9588  0.999...  11686  cos2bnd  11925  sincos2sgn  11931  slotsdifplendx  12887  dsndxntsetndx  12897  unifndxntsetndx  12904  setsmsdsg  14716  2logb9irr  15207  2logb9irrap  15213