Theorem 7re 9090

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 9071	. 2 ⊢ 7 = (6 + 1)
2		6re 9088	. . 3 ⊢ 6 ∈ ℝ
3		1re 8042	. . 3 ⊢ 1 ∈ ℝ
4	2, 3	readdcli 8056	. 2 ⊢ (6 + 1) ∈ ℝ
5	1, 4	eqeltri 2269	1 ⊢ 7 ∈ ℝ

Syntax hints:   ∈ wcel 2167  (class class class)co 5925  ℝcr 7895  1c1 7897   + caddc 7899  6c6 9062  7c7 9063

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 1461  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-4 1524  ax-17 1540  ax-ial 1548  ax-ext 2178  ax-1re 7990  ax-addrcl 7993

This theorem depends on definitions:  df-bi 117  df-cleq 2189  df-clel 2192  df-2 9066  df-3 9067  df-4 9068  df-5 9069  df-6 9070  df-7 9071

This theorem is referenced by:  7cn  9091  8re  9092  8pos  9110  5lt7  9193  4lt7  9194  3lt7  9195  2lt7  9196  1lt7  9197  7lt8  9198  6lt8  9199  7lt9  9206  6lt9  9207  7lt10  9606  6lt10  9607  lgsdir2lem1  15353