Theorem 6re 8825

Description: The number 6 is real. (Contributed by NM, 27-May-1999.)

Assertion

Ref	Expression
6re	|- 6 e. RR

Proof of Theorem 6re

Step	Hyp	Ref	Expression
1		df-6 8807	. 2 |- 6 = ( 5 + 1 )
2		5re 8823	. . 3 |- 5 e. RR
3		1re 7789	. . 3 |- 1 e. RR
4	2, 3	readdcli 7803	. 2 |- ( 5 + 1 ) e. RR
5	1, 4	eqeltri 2213	1 |- 6 e. RR

Syntax hints:   e. wcel 1481  (class class class)co 5782   RRcr 7643   1c1 7645   + caddc 7647   5c5 8798   6c6 8799

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  df-6 8807

This theorem is referenced by:  6cn  8826  7re  8827  7pos  8846  4lt6  8924  3lt6  8925  2lt6  8926  1lt6  8927  6lt7  8928  5lt7  8929  6lt8  8935  5lt8  8936  6lt9  8943  5lt9  8944  8th4div3  8963  halfpm6th  8964  div4p1lem1div2  8997  6lt10  9339  5lt10  9340  5recm6rec  9349  efi4p  11460  resin4p  11461  recos4p  11462  ef01bndlem  11499  sin01bnd  11500  cos01bnd  11501  sincos6thpi  12971  pigt3  12973