Theorem 5re 8823

Description: The number 5 is real. (Contributed by NM, 27-May-1999.)

Assertion

Ref	Expression
5re	|- 5 e. RR

Proof of Theorem 5re

Step	Hyp	Ref	Expression
1		df-5 8806	. 2 |- 5 = ( 4 + 1 )
2		4re 8821	. . 3 |- 4 e. RR
3		1re 7789	. . 3 |- 1 e. RR
4	2, 3	readdcli 7803	. 2 |- ( 4 + 1 ) e. RR
5	1, 4	eqeltri 2213	1 |- 5 e. RR

Syntax hints:   e. wcel 1481  (class class class)co 5782   RRcr 7643   1c1 7645   + caddc 7647   4c4 8797   5c5 8798

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-4 1488  ax-17 1507  ax-ial 1515  ax-ext 2122  ax-1re 7738  ax-addrcl 7741

This theorem depends on definitions:  df-bi 116  df-cleq 2133  df-clel 2136  df-2 8803  df-3 8804  df-4 8805  df-5 8806

This theorem is referenced by:  5cn  8824  6re  8825  6pos  8845  3lt5  8920  2lt5  8921  1lt5  8922  5lt6  8923  4lt6  8924  5lt7  8929  4lt7  8930  5lt8  8936  4lt8  8937  5lt9  8944  4lt9  8945  5lt10  9340  4lt10  9341  5recm6rec  9349  ef01bndlem  11499