Theorem 7re 7998

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 7978	. 2 |- 7 = ( 6 + 1 )
2		6re 7996	. . 3 |- 6 e. RR
3		1re 7026	. . 3 |- 1 e. RR
4	2, 3	readdcli 7040	. 2 |- ( 6 + 1 ) e. RR
5	1, 4	eqeltri 2110	1 |- 7 e. RR

Syntax hints:   e. wcel 1393  (class class class)co 5512   RRcr 6888   1c1 6890   + caddc 6892   6c6 7968   7c7 7969

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

This theorem is referenced by:  7cn  7999  8re  8000  8pos  8019  5lt7  8102  4lt7  8103  3lt7  8104  2lt7  8105  1lt7  8106  7lt8  8107  6lt8  8108  7lt9  8115  6lt9  8116  7lt10  8124  6lt10  8125