Theorem 7re 9154

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 9135	. 2 |- 7 = ( 6 + 1 )
2		6re 9152	. . 3 |- 6 e. RR
3		1re 8106	. . 3 |- 1 e. RR
4	2, 3	readdcli 8120	. 2 |- ( 6 + 1 ) e. RR
5	1, 4	eqeltri 2280	1 |- 7 e. RR

Syntax hints:   e. wcel 2178  (class class class)co 5967   RRcr 7959   1c1 7961   + caddc 7963   6c6 9126   7c7 9127

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 1471  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-4 1534  ax-17 1550  ax-ial 1558  ax-ext 2189  ax-1re 8054  ax-addrcl 8057

This theorem depends on definitions:  df-bi 117  df-cleq 2200  df-clel 2203  df-2 9130  df-3 9131  df-4 9132  df-5 9133  df-6 9134  df-7 9135

This theorem is referenced by:  7cn  9155  8re  9156  8pos  9174  5lt7  9257  4lt7  9258  3lt7  9259  2lt7  9260  1lt7  9261  7lt8  9262  6lt8  9263  7lt9  9270  6lt9  9271  7lt10  9671  6lt10  9672  lgsdir2lem1  15620