Theorem 7re 9216

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 9197	. 2 ⊢ 7 = (6 + 1)
2		6re 9214	. . 3 ⊢ 6 ∈ ℝ
3		1re 8168	. . 3 ⊢ 1 ∈ ℝ
4	2, 3	readdcli 8182	. 2 ⊢ (6 + 1) ∈ ℝ
5	1, 4	eqeltri 2302	1 ⊢ 7 ∈ ℝ

Syntax hints:   ∈ wcel 2200  (class class class)co 6013  ℝcr 8021  1c1 8023   + caddc 8025  6c6 9188  7c7 9189

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 8116  ax-addrcl 8119

This theorem depends on definitions:  df-bi 117  df-cleq 2222  df-clel 2225  df-2 9192  df-3 9193  df-4 9194  df-5 9195  df-6 9196  df-7 9197

This theorem is referenced by:  7cn  9217  8re  9218  8pos  9236  5lt7  9319  4lt7  9320  3lt7  9321  2lt7  9322  1lt7  9323  7lt8  9324  6lt8  9325  7lt9  9332  6lt9  9333  7lt10  9733  6lt10  9734  lgsdir2lem1  15747