Theorem 7re 9020

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 9001	. 2 ⊢ 7 = (6 + 1)
2		6re 9018	. . 3 ⊢ 6 ∈ ℝ
3		1re 7974	. . 3 ⊢ 1 ∈ ℝ
4	2, 3	readdcli 7988	. 2 ⊢ (6 + 1) ∈ ℝ
5	1, 4	eqeltri 2262	1 ⊢ 7 ∈ ℝ

Syntax hints:   ∈ wcel 2160  (class class class)co 5891  ℝcr 7828  1c1 7830   + caddc 7832  6c6 8992  7c7 8993

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 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-17 1537  ax-ial 1545  ax-ext 2171  ax-1re 7923  ax-addrcl 7926

This theorem depends on definitions:  df-bi 117  df-cleq 2182  df-clel 2185  df-2 8996  df-3 8997  df-4 8998  df-5 8999  df-6 9000  df-7 9001

This theorem is referenced by:  7cn  9021  8re  9022  8pos  9040  5lt7  9122  4lt7  9123  3lt7  9124  2lt7  9125  1lt7  9126  7lt8  9127  6lt8  9128  7lt9  9135  6lt9  9136  7lt10  9534  6lt10  9535  lgsdir2lem1  14813