Theorem 7re 8568

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 8549	. 2 ⊢ 7 = (6 + 1)
2		6re 8566	. . 3 ⊢ 6 ∈ ℝ
3		1re 7550	. . 3 ⊢ 1 ∈ ℝ
4	2, 3	readdcli 7564	. 2 ⊢ (6 + 1) ∈ ℝ
5	1, 4	eqeltri 2161	1 ⊢ 7 ∈ ℝ

Syntax hints:   ∈ wcel 1439  (class class class)co 5668  ℝcr 7412  1c1 7414   + caddc 7416  6c6 8540  7c7 8541

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1382  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-4 1446  ax-17 1465  ax-ial 1473  ax-ext 2071  ax-1re 7502  ax-addrcl 7505

This theorem depends on definitions:  df-bi 116  df-cleq 2082  df-clel 2085  df-2 8544  df-3 8545  df-4 8546  df-5 8547  df-6 8548  df-7 8549

This theorem is referenced by:  7cn  8569  8re  8570  8pos  8588  5lt7  8664  4lt7  8665  3lt7  8666  2lt7  8667  1lt7  8668  7lt8  8669  6lt8  8670  7lt9  8677  6lt9  8678  7lt10  9072  6lt10  9073