Theorem 7re 9337

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 9318	. 2 ⊢ 7 = (6 + 1)
2		6re 9335	. . 3 ⊢ 6 ∈ ℝ
3		1re 8289	. . 3 ⊢ 1 ∈ ℝ
4	2, 3	readdcli 8303	. 2 ⊢ (6 + 1) ∈ ℝ
5	1, 4	eqeltri 2307	1 ⊢ 7 ∈ ℝ

Syntax hints:   ∈ wcel 2205  (class class class)co 6058  ℝcr 8142  1c1 8144   + caddc 8146  6c6 9309  7c7 9310

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 1496  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-4 1559  ax-17 1575  ax-ial 1583  ax-ext 2216  ax-1re 8237  ax-addrcl 8240

This theorem depends on definitions:  df-bi 117  df-cleq 2227  df-clel 2230  df-2 9313  df-3 9314  df-4 9315  df-5 9316  df-6 9317  df-7 9318

This theorem is referenced by:  7cn  9338  8re  9339  8pos  9357  5lt7  9440  4lt7  9441  3lt7  9442  2lt7  9443  1lt7  9444  7lt8  9445  6lt8  9446  7lt9  9453  6lt9  9454  7lt10  9859  6lt10  9860  lgsdir2lem1  16027