Theorem 7re 9121

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 9102	. 2 |- 7 = ( 6 + 1 )
2		6re 9119	. . 3 |- 6 e. RR
3		1re 8073	. . 3 |- 1 e. RR
4	2, 3	readdcli 8087	. 2 |- ( 6 + 1 ) e. RR
5	1, 4	eqeltri 2278	1 |- 7 e. RR

Syntax hints:   e. wcel 2176  (class class class)co 5946   RRcr 7926   1c1 7928   + caddc 7930   6c6 9093   7c7 9094

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 1470  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-4 1533  ax-17 1549  ax-ial 1557  ax-ext 2187  ax-1re 8021  ax-addrcl 8024

This theorem depends on definitions:  df-bi 117  df-cleq 2198  df-clel 2201  df-2 9097  df-3 9098  df-4 9099  df-5 9100  df-6 9101  df-7 9102

This theorem is referenced by:  7cn  9122  8re  9123  8pos  9141  5lt7  9224  4lt7  9225  3lt7  9226  2lt7  9227  1lt7  9228  7lt8  9229  6lt8  9230  7lt9  9237  6lt9  9238  7lt10  9638  6lt10  9639  lgsdir2lem1  15538