Theorem 7re 9320

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 9301	. 2 ⊢ 7 = (6 + 1)
2		6re 9318	. . 3 ⊢ 6 ∈ ℝ
3		1re 8273	. . 3 ⊢ 1 ∈ ℝ
4	2, 3	readdcli 8287	. 2 ⊢ (6 + 1) ∈ ℝ
5	1, 4	eqeltri 2305	1 ⊢ 7 ∈ ℝ

Syntax hints:   ∈ wcel 2203  (class class class)co 6050  ℝcr 8126  1c1 8128   + caddc 8130  6c6 9292  7c7 9293

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 2214  ax-1re 8221  ax-addrcl 8224

This theorem depends on definitions:  df-bi 117  df-cleq 2225  df-clel 2228  df-2 9296  df-3 9297  df-4 9298  df-5 9299  df-6 9300  df-7 9301

This theorem is referenced by:  7cn  9321  8re  9322  8pos  9340  5lt7  9423  4lt7  9424  3lt7  9425  2lt7  9426  1lt7  9427  7lt8  9428  6lt8  9429  7lt9  9436  6lt9  9437  7lt10  9841  6lt10  9842  lgsdir2lem1  15901