Theorem 7re 9055

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 9036	. 2 ⊢ 7 = (6 + 1)
2		6re 9053	. . 3 ⊢ 6 ∈ ℝ
3		1re 8008	. . 3 ⊢ 1 ∈ ℝ
4	2, 3	readdcli 8022	. 2 ⊢ (6 + 1) ∈ ℝ
5	1, 4	eqeltri 2266	1 ⊢ 7 ∈ ℝ

Syntax hints:   ∈ wcel 2164  (class class class)co 5910  ℝcr 7861  1c1 7863   + caddc 7865  6c6 9027  7c7 9028

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 7956  ax-addrcl 7959

This theorem depends on definitions:  df-bi 117  df-cleq 2186  df-clel 2189  df-2 9031  df-3 9032  df-4 9033  df-5 9034  df-6 9035  df-7 9036

This theorem is referenced by:  7cn  9056  8re  9057  8pos  9075  5lt7  9157  4lt7  9158  3lt7  9159  2lt7  9160  1lt7  9161  7lt8  9162  6lt8  9163  7lt9  9170  6lt9  9171  7lt10  9570  6lt10  9571  lgsdir2lem1  15086