Theorem 7re 9366

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 9347	. 2 ⊢ 7 = (6 + 1)
2		6re 9364	. . 3 ⊢ 6 ∈ ℝ
3		1re 8315	. . 3 ⊢ 1 ∈ ℝ
4	2, 3	readdcli 8329	. 2 ⊢ (6 + 1) ∈ ℝ
5	1, 4	eqeltri 2311	1 ⊢ 7 ∈ ℝ

Syntax hints:   ∈ wcel 2209  (class class class)co 6075  ℝcr 8168  1c1 8170   + caddc 8172  6c6 9338  7c7 9339

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 1500  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-4 1563  ax-17 1579  ax-ial 1587  ax-ext 2220  ax-1re 8263  ax-addrcl 8266

This theorem depends on definitions:  df-bi 117  df-cleq 2231  df-clel 2234  df-2 9342  df-3 9343  df-4 9344  df-5 9345  df-6 9346  df-7 9347

This theorem is referenced by:  7cn  9367  8re  9368  8pos  9386  5lt7  9469  4lt7  9470  3lt7  9471  2lt7  9472  1lt7  9473  7lt8  9474  6lt8  9475  7lt9  9482  6lt9  9483  7lt10  9888  6lt10  9889  lgsdir2lem1  16061