Theorem 7re 9389

Description: The number 7 is real. (Contributed by NM, 27-May-1999.)

Assertion

Ref	Expression
7re	|- 7 e. RR

Proof of Theorem 7re

Step	Hyp	Ref	Expression
1		df-7 9370	. 2 |- 7 = ( 6 + 1 )
2		6re 9387	. . 3 |- 6 e. RR
3		1re 8325	. . 3 |- 1 e. RR
4	2, 3	readdcli 8339	. 2 |- ( 6 + 1 ) e. RR
5	1, 4	eqeltri 2311	1 |- 7 e. RR

This proof depends on syntax axioms:   e. wcel 2209  (class class class)co 6085   RRcr 8178   1c1 8180   + caddc 8182   6c6 9361   7c7 9362

This proof depends on 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 8273  ax-addrcl 8276

This proof depends on definitions:  df-bi 117  df-cleq 2231  df-clel 2234  df-2 9365  df-3 9366  df-4 9367  df-5 9368  df-6 9369  df-7 9370

This theorem is used by:  7cn  9390  8re  9391  8pos  9409  5lt7  9494  4lt7  9495  3lt7  9496  2lt7  9497  1lt7  9498  7lt8  9499  6lt8  9500  7lt9  9507  6lt9  9508  7lt10  9918  6lt10  9919  lgsdir2lem1  16245