Theorem 7re 9387

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 9368	. 2 ⊢ 7 = (6 + 1)
2		6re 9385	. . 3 ⊢ 6 ∈ ℝ
3		1re 8325	. . 3 ⊢ 1 ∈ ℝ
4	2, 3	readdcli 8339	. 2 ⊢ (6 + 1) ∈ ℝ
5	1, 4	eqeltri 2311	1 ⊢ 7 ∈ ℝ

This proof depends on syntax axioms:   ∈ wcel 2209  (class class class)co 6085  ℝcr 8178  1c1 8180   + caddc 8182  6c6 9359  7c7 9360

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1500  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-4 1563  ax-17 1579  ax-ial 1587  ax-ext 2220  ax-1re 8273  ax-addrcl 8276

This proof depends on definitions:  df-bi 117  df-cleq 2231  df-clel 2234  df-2 9363  df-3 9364  df-4 9365  df-5 9366  df-6 9367  df-7 9368

This theorem is used by:  7cn  9388  8re  9389  8pos  9407  5lt7  9490  4lt7  9491  3lt7  9492  2lt7  9493  1lt7  9494  7lt8  9495  6lt8  9496  7lt9  9503  6lt9  9504  7lt10  9909  6lt10  9910  lgsdir2lem1  16147