Theorem 9re 8717

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 8696	. 2 |- 9 = ( 8 + 1 )
2		8re 8715	. . 3 |- 8 e. RR
3		1re 7689	. . 3 |- 1 e. RR
4	2, 3	readdcli 7703	. 2 |- ( 8 + 1 ) e. RR
5	1, 4	eqeltri 2187	1 |- 9 e. RR

Syntax hints:   e. wcel 1463  (class class class)co 5728   RRcr 7546   1c1 7548   + caddc 7550   8c8 8687   9c9 8688

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-4 1470  ax-17 1489  ax-ial 1497  ax-ext 2097  ax-1re 7639  ax-addrcl 7642

This theorem depends on definitions:  df-bi 116  df-cleq 2108  df-clel 2111  df-2 8689  df-3 8690  df-4 8691  df-5 8692  df-6 8693  df-7 8694  df-8 8695  df-9 8696

This theorem is referenced by:  9cn  8718  7lt9  8822  6lt9  8823  5lt9  8824  4lt9  8825  3lt9  8826  2lt9  8827  1lt9  8828  9lt10  9216  8lt10  9217  0.999...  11182  cos2bnd  11318  sincos2sgn  11323  setsmsdsg  12469