Theorem 7re 9002

Description: The number 7 is real. (Contributed by NM, 27-May-1999.)

Assertion

Ref	Expression
7re	⊢ 7 ∈ ℝ

Proof of Theorem 7re

Step	Hyp	Ref	Expression
1		df-7 8983	. 2 ⊢ 7 = (6 + 1)
2		6re 9000	. . 3 ⊢ 6 ∈ ℝ
3		1re 7956	. . 3 ⊢ 1 ∈ ℝ
4	2, 3	readdcli 7970	. 2 ⊢ (6 + 1) ∈ ℝ
5	1, 4	eqeltri 2250	1 ⊢ 7 ∈ ℝ

Syntax hints:   ∈ wcel 2148  (class class class)co 5875  ℝcr 7810  1c1 7812   + caddc 7814  6c6 8974  7c7 8975

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 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-17 1526  ax-ial 1534  ax-ext 2159  ax-1re 7905  ax-addrcl 7908

This theorem depends on definitions:  df-bi 117  df-cleq 2170  df-clel 2173  df-2 8978  df-3 8979  df-4 8980  df-5 8981  df-6 8982  df-7 8983

This theorem is referenced by:  7cn  9003  8re  9004  8pos  9022  5lt7  9104  4lt7  9105  3lt7  9106  2lt7  9107  1lt7  9108  7lt8  9109  6lt8  9110  7lt9  9117  6lt9  9118  7lt10  9516  6lt10  9517  lgsdir2lem1  14432