Theorem 7re 9016

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 8997	. 2 |- 7 = ( 6 + 1 )
2		6re 9014	. . 3 |- 6 e. RR
3		1re 7970	. . 3 |- 1 e. RR
4	2, 3	readdcli 7984	. 2 |- ( 6 + 1 ) e. RR
5	1, 4	eqeltri 2260	1 |- 7 e. RR

Syntax hints:   e. wcel 2158  (class class class)co 5888   RRcr 7824   1c1 7826   + caddc 7828   6c6 8988   7c7 8989

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 1457  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-4 1520  ax-17 1536  ax-ial 1544  ax-ext 2169  ax-1re 7919  ax-addrcl 7922

This theorem depends on definitions:  df-bi 117  df-cleq 2180  df-clel 2183  df-2 8992  df-3 8993  df-4 8994  df-5 8995  df-6 8996  df-7 8997

This theorem is referenced by:  7cn  9017  8re  9018  8pos  9036  5lt7  9118  4lt7  9119  3lt7  9120  2lt7  9121  1lt7  9122  7lt8  9123  6lt8  9124  7lt9  9131  6lt9  9132  7lt10  9530  6lt10  9531  lgsdir2lem1  14725