Theorem 7re 9322

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 9303	. 2 ⊢ 7 = (6 + 1)
2		6re 9320	. . 3 ⊢ 6 ∈ ℝ
3		1re 8275	. . 3 ⊢ 1 ∈ ℝ
4	2, 3	readdcli 8289	. 2 ⊢ (6 + 1) ∈ ℝ
5	1, 4	eqeltri 2307	1 ⊢ 7 ∈ ℝ

Syntax hints:   ∈ wcel 2205  (class class class)co 6052  ℝcr 8128  1c1 8130   + caddc 8132  6c6 9294  7c7 9295

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 8223  ax-addrcl 8226

This theorem depends on definitions:  df-bi 117  df-cleq 2227  df-clel 2230  df-2 9298  df-3 9299  df-4 9300  df-5 9301  df-6 9302  df-7 9303

This theorem is referenced by:  7cn  9323  8re  9324  8pos  9342  5lt7  9425  4lt7  9426  3lt7  9427  2lt7  9428  1lt7  9429  7lt8  9430  6lt8  9431  7lt9  9438  6lt9  9439  7lt10  9844  6lt10  9845  lgsdir2lem1  15918