Theorem 6re 9364

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

Assertion

Ref	Expression
6re	⊢ 6 ∈ ℝ

Proof of Theorem 6re

Step	Hyp	Ref	Expression
1		df-6 9346	. 2 ⊢ 6 = (5 + 1)
2		5re 9362	. . 3 ⊢ 5 ∈ ℝ
3		1re 8315	. . 3 ⊢ 1 ∈ ℝ
4	2, 3	readdcli 8329	. 2 ⊢ (5 + 1) ∈ ℝ
5	1, 4	eqeltri 2311	1 ⊢ 6 ∈ ℝ

Syntax hints:   ∈ wcel 2209  (class class class)co 6075  ℝcr 8168  1c1 8170   + caddc 8172  5c5 9337  6c6 9338

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 1500  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-4 1563  ax-17 1579  ax-ial 1587  ax-ext 2220  ax-1re 8263  ax-addrcl 8266

This theorem depends on definitions:  df-bi 117  df-cleq 2231  df-clel 2234  df-2 9342  df-3 9343  df-4 9344  df-5 9345  df-6 9346

This theorem is referenced by:  6cn  9365  7re  9366  7pos  9385  4lt6  9464  3lt6  9465  2lt6  9466  1lt6  9467  6lt7  9468  5lt7  9469  6lt8  9475  5lt8  9476  6lt9  9483  5lt9  9484  8th4div3  9503  halfpm6th  9504  div4p1lem1div2  9538  6lt10  9889  5lt10  9890  5recm6rec  9899  efi4p  12462  resin4p  12463  recos4p  12464  ef01bndlem  12501  sin01bnd  12502  cos01bnd  12503  slotsdifipndx  13506  slotstnscsi  13526  plendxnvscandx  13540  slotsdnscsi  13554  sincos6thpi  15866  pigt3  15868