Theorem 7re 8178

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 8159	. 2 ⊢ 7 = (6 + 1)
2		6re 8176	. . 3 ⊢ 6 ∈ ℝ
3		1re 7169	. . 3 ⊢ 1 ∈ ℝ
4	2, 3	readdcli 7183	. 2 ⊢ (6 + 1) ∈ ℝ
5	1, 4	eqeltri 2152	1 ⊢ 7 ∈ ℝ

Syntax hints:   ∈ wcel 1434  (class class class)co 5537  ℝcr 7031  1c1 7033   + caddc 7035  6c6 8149  7c7 8150

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-17 1460  ax-ial 1468  ax-ext 2064  ax-1re 7121  ax-addrcl 7124

This theorem depends on definitions:  df-bi 115  df-cleq 2075  df-clel 2078  df-2 8154  df-3 8155  df-4 8156  df-5 8157  df-6 8158  df-7 8159

This theorem is referenced by:  7cn  8179  8re  8180  8pos  8198  5lt7  8273  4lt7  8274  3lt7  8275  2lt7  8276  1lt7  8277  7lt8  8278  6lt8  8279  7lt9  8286  6lt9  8287  7lt10  8679  6lt10  8680