Theorem 7re 9067

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 9048	. 2 ⊢ 7 = (6 + 1)
2		6re 9065	. . 3 ⊢ 6 ∈ ℝ
3		1re 8020	. . 3 ⊢ 1 ∈ ℝ
4	2, 3	readdcli 8034	. 2 ⊢ (6 + 1) ∈ ℝ
5	1, 4	eqeltri 2266	1 ⊢ 7 ∈ ℝ

Syntax hints:   ∈ wcel 2164  (class class class)co 5919  ℝcr 7873  1c1 7875   + caddc 7877  6c6 9039  7c7 9040

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 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-17 1537  ax-ial 1545  ax-ext 2175  ax-1re 7968  ax-addrcl 7971

This theorem depends on definitions:  df-bi 117  df-cleq 2186  df-clel 2189  df-2 9043  df-3 9044  df-4 9045  df-5 9046  df-6 9047  df-7 9048

This theorem is referenced by:  7cn  9068  8re  9069  8pos  9087  5lt7  9170  4lt7  9171  3lt7  9172  2lt7  9173  1lt7  9174  7lt8  9175  6lt8  9176  7lt9  9183  6lt9  9184  7lt10  9583  6lt10  9584  lgsdir2lem1  15176