Theorem 9re 8193

Description: The number 9 is real. (Contributed by NM, 27-May-1999.)

Assertion

Ref	Expression
9re	⊢ 9 ∈ ℝ

Proof of Theorem 9re

Step	Hyp	Ref	Expression
1		df-9 8172	. 2 ⊢ 9 = (8 + 1)
2		8re 8191	. . 3 ⊢ 8 ∈ ℝ
3		1re 7180	. . 3 ⊢ 1 ∈ ℝ
4	2, 3	readdcli 7194	. 2 ⊢ (8 + 1) ∈ ℝ
5	1, 4	eqeltri 2152	1 ⊢ 9 ∈ ℝ

Syntax hints:   ∈ wcel 1434  (class class class)co 5543  ℝcr 7042  1c1 7044   + caddc 7046  8c8 8162  9c9 8163

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-17 1460  ax-ial 1468  ax-ext 2064  ax-1re 7132  ax-addrcl 7135

This theorem depends on definitions:  df-bi 115  df-cleq 2075  df-clel 2078  df-2 8165  df-3 8166  df-4 8167  df-5 8168  df-6 8169  df-7 8170  df-8 8171  df-9 8172

This theorem is referenced by:  9cn  8194  7lt9  8297  6lt9  8298  5lt9  8299  4lt9  8300  3lt9  8301  2lt9  8302  1lt9  8303  9lt10  8688  8lt10  8689