Theorem 7re 9225

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 9206	. 2 ⊢ 7 = (6 + 1)
2		6re 9223	. . 3 ⊢ 6 ∈ ℝ
3		1re 8177	. . 3 ⊢ 1 ∈ ℝ
4	2, 3	readdcli 8191	. 2 ⊢ (6 + 1) ∈ ℝ
5	1, 4	eqeltri 2304	1 ⊢ 7 ∈ ℝ

Syntax hints:   ∈ wcel 2202  (class class class)co 6017  ℝcr 8030  1c1 8032   + caddc 8034  6c6 9197  7c7 9198

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 1495  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-4 1558  ax-17 1574  ax-ial 1582  ax-ext 2213  ax-1re 8125  ax-addrcl 8128

This theorem depends on definitions:  df-bi 117  df-cleq 2224  df-clel 2227  df-2 9201  df-3 9202  df-4 9203  df-5 9204  df-6 9205  df-7 9206

This theorem is referenced by:  7cn  9226  8re  9227  8pos  9245  5lt7  9328  4lt7  9329  3lt7  9330  2lt7  9331  1lt7  9332  7lt8  9333  6lt8  9334  7lt9  9341  6lt9  9342  7lt10  9742  6lt10  9743  lgsdir2lem1  15756