Theorem 10re 8004

Description: The number 10 is real. (Contributed by NM, 5-Feb-2007.)

Assertion

Ref	Expression
10re	⊢ 10 ∈ ℝ

Proof of Theorem 10re

Step	Hyp	Ref	Expression
1		df-10 7981	. 2 ⊢ 10 = (9 + 1)
2		9re 8002	. . 3 ⊢ 9 ∈ ℝ
3		1re 7026	. . 3 ⊢ 1 ∈ ℝ
4	2, 3	readdcli 7040	. 2 ⊢ (9 + 1) ∈ ℝ
5	1, 4	eqeltri 2110	1 ⊢ 10 ∈ ℝ

Syntax hints:   ∈ wcel 1393  (class class class)co 5512  ℝcr 6888  1c1 6890   + caddc 6892  9c9 7971  10c10 7972

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427  ax-ext 2022  ax-1re 6978  ax-addrcl 6981

This theorem depends on definitions:  df-bi 110  df-cleq 2033  df-clel 2036  df-2 7973  df-3 7974  df-4 7975  df-5 7976  df-6 7977  df-7 7978  df-8 7979  df-9 7980  df-10 7981

This theorem is referenced by:  8lt10  8123  7lt10  8124  6lt10  8125  5lt10  8126  4lt10  8127  3lt10  8128  2lt10  8129  1lt10  8130