Theorem 7re 9073

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 9054	. 2 |- 7 = ( 6 + 1 )
2		6re 9071	. . 3 |- 6 e. RR
3		1re 8025	. . 3 |- 1 e. RR
4	2, 3	readdcli 8039	. 2 |- ( 6 + 1 ) e. RR
5	1, 4	eqeltri 2269	1 |- 7 e. RR

Syntax hints:   e. wcel 2167  (class class class)co 5922   RRcr 7878   1c1 7880   + caddc 7882   6c6 9045   7c7 9046

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 1461  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-4 1524  ax-17 1540  ax-ial 1548  ax-ext 2178  ax-1re 7973  ax-addrcl 7976

This theorem depends on definitions:  df-bi 117  df-cleq 2189  df-clel 2192  df-2 9049  df-3 9050  df-4 9051  df-5 9052  df-6 9053  df-7 9054

This theorem is referenced by:  7cn  9074  8re  9075  8pos  9093  5lt7  9176  4lt7  9177  3lt7  9178  2lt7  9179  1lt7  9180  7lt8  9181  6lt8  9182  7lt9  9189  6lt9  9190  7lt10  9589  6lt10  9590  lgsdir2lem1  15269