Theorem 5re 9333

Description: The number 5 is real. (Contributed by NM, 27-May-1999.)

Assertion

Ref	Expression
5re	⊢ 5 ∈ ℝ

Proof of Theorem 5re

Step	Hyp	Ref	Expression
1		df-5 9316	. 2 ⊢ 5 = (4 + 1)
2		4re 9331	. . 3 ⊢ 4 ∈ ℝ
3		1re 8289	. . 3 ⊢ 1 ∈ ℝ
4	2, 3	readdcli 8303	. 2 ⊢ (4 + 1) ∈ ℝ
5	1, 4	eqeltri 2307	1 ⊢ 5 ∈ ℝ

Syntax hints:   ∈ wcel 2205  (class class class)co 6058  ℝcr 8142  1c1 8144   + caddc 8146  4c4 9307  5c5 9308

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 1496  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-4 1559  ax-17 1575  ax-ial 1583  ax-ext 2216  ax-1re 8237  ax-addrcl 8240

This theorem depends on definitions:  df-bi 117  df-cleq 2227  df-clel 2230  df-2 9313  df-3 9314  df-4 9315  df-5 9316

This theorem is referenced by:  5cn  9334  6re  9335  6pos  9355  3lt5  9431  2lt5  9432  1lt5  9433  5lt6  9434  4lt6  9435  5lt7  9440  4lt7  9441  5lt8  9447  4lt8  9448  5lt9  9455  4lt9  9456  5lt10  9861  4lt10  9862  5recm6rec  9870  5eluz3  9911  ef01bndlem  12467  vscandxnscandx  13459  slotsdifipndx  13472  slotstnscsi  13492  plendxnscandx  13505  slotsdnscsi  13520  lgsdir2lem1  16027  gausslemma2dlem4  16063  2lgslem3  16100