Theorem 6re 9335

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 9317	. 2 |- 6 = ( 5 + 1 )
2		5re 9333	. . 3 |- 5 e. RR
3		1re 8289	. . 3 |- 1 e. RR
4	2, 3	readdcli 8303	. 2 |- ( 5 + 1 ) e. RR
5	1, 4	eqeltri 2307	1 |- 6 e. RR

Syntax hints:   e. wcel 2205  (class class class)co 6058   RRcr 8142   1c1 8144   + caddc 8146   5c5 9308   6c6 9309

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 1496  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-4 1559  ax-17 1575  ax-ial 1583  ax-ext 2216  ax-1re 8237  ax-addrcl 8240

This theorem depends on definitions:  df-bi 117  df-cleq 2227  df-clel 2230  df-2 9313  df-3 9314  df-4 9315  df-5 9316  df-6 9317

This theorem is referenced by:  6cn  9336  7re  9337  7pos  9356  4lt6  9435  3lt6  9436  2lt6  9437  1lt6  9438  6lt7  9439  5lt7  9440  6lt8  9446  5lt8  9447  6lt9  9454  5lt9  9455  8th4div3  9474  halfpm6th  9475  div4p1lem1div2  9509  6lt10  9860  5lt10  9861  5recm6rec  9870  efi4p  12428  resin4p  12429  recos4p  12430  ef01bndlem  12467  sin01bnd  12468  cos01bnd  12469  slotsdifipndx  13472  slotstnscsi  13492  plendxnvscandx  13506  slotsdnscsi  13520  sincos6thpi  15833  pigt3  15835