Theorem 7re 9204

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 9185	. 2 ⊢ 7 = (6 + 1)
2		6re 9202	. . 3 ⊢ 6 ∈ ℝ
3		1re 8156	. . 3 ⊢ 1 ∈ ℝ
4	2, 3	readdcli 8170	. 2 ⊢ (6 + 1) ∈ ℝ
5	1, 4	eqeltri 2302	1 ⊢ 7 ∈ ℝ

Syntax hints:   ∈ wcel 2200  (class class class)co 6007  ℝcr 8009  1c1 8011   + caddc 8013  6c6 9176  7c7 9177

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 1493  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-4 1556  ax-17 1572  ax-ial 1580  ax-ext 2211  ax-1re 8104  ax-addrcl 8107

This theorem depends on definitions:  df-bi 117  df-cleq 2222  df-clel 2225  df-2 9180  df-3 9181  df-4 9182  df-5 9183  df-6 9184  df-7 9185

This theorem is referenced by:  7cn  9205  8re  9206  8pos  9224  5lt7  9307  4lt7  9308  3lt7  9309  2lt7  9310  1lt7  9311  7lt8  9312  6lt8  9313  7lt9  9320  6lt9  9321  7lt10  9721  6lt10  9722  lgsdir2lem1  15722