Theorem 7re 8043

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 8024	. 2 ⊢ 7 = (6 + 1)
2		6re 8041	. . 3 ⊢ 6 ∈ ℝ
3		1re 7054	. . 3 ⊢ 1 ∈ ℝ
4	2, 3	readdcli 7068	. 2 ⊢ (6 + 1) ∈ ℝ
5	1, 4	eqeltri 2124	1 ⊢ 7 ∈ ℝ

Syntax hints:   ∈ wcel 1407  (class class class)co 5537  ℝcr 6916  1c1 6918   + caddc 6920  6c6 8014  7c7 8015

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1350  ax-gen 1352  ax-ie1 1396  ax-ie2 1397  ax-4 1414  ax-17 1433  ax-ial 1441  ax-ext 2036  ax-1re 7006  ax-addrcl 7009

This theorem depends on definitions:  df-bi 114  df-cleq 2047  df-clel 2050  df-2 8019  df-3 8020  df-4 8021  df-5 8022  df-6 8023  df-7 8024

This theorem is referenced by:  7cn  8044  8re  8045  8pos  8063  5lt7  8138  4lt7  8139  3lt7  8140  2lt7  8141  1lt7  8142  7lt8  8143  6lt8  8144  7lt9  8151  6lt9  8152  7lt10  8529  6lt10  8530