Theorem 6p2e8 9260

Description: 6 + 2 = 8. (Contributed by NM, 11-May-2004.)

Assertion

Ref	Expression
6p2e8	|- ( 6 + 2 ) = 8

Proof of Theorem 6p2e8

Step	Hyp	Ref	Expression
1		df-2 9169	. . . . 5 |- 2 = ( 1 + 1 )
2	1	oveq2i 6012	. . . 4 |- ( 6 + 2 ) = ( 6 + ( 1 + 1 ) )
3		6cn 9192	. . . . 5 |- 6 e. CC
4		ax-1cn 8092	. . . . 5 |- 1 e. CC
5	3, 4, 4	addassi 8154	. . . 4 |- ( ( 6 + 1 ) + 1 ) = ( 6 + ( 1 + 1 ) )
6	2, 5	eqtr4i 2253	. . 3 |- ( 6 + 2 ) = ( ( 6 + 1 ) + 1 )
7		df-7 9174	. . . 4 |- 7 = ( 6 + 1 )
8	7	oveq1i 6011	. . 3 |- ( 7 + 1 ) = ( ( 6 + 1 ) + 1 )
9	6, 8	eqtr4i 2253	. 2 |- ( 6 + 2 ) = ( 7 + 1 )
10		df-8 9175	. 2 |- 8 = ( 7 + 1 )
11	9, 10	eqtr4i 2253	1 |- ( 6 + 2 ) = 8

Syntax hints:   = wceq 1395  (class class class)co 6001   1c1 8000   + caddc 8002   2c2 9161   6c6 9165   7c7 9166   8c8 9167

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-io 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211  ax-resscn 8091  ax-1cn 8092  ax-1re 8093  ax-addrcl 8096  ax-addass 8101

This theorem depends on definitions:  df-bi 117  df-3an 1004  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-rex 2514  df-v 2801  df-un 3201  df-in 3203  df-ss 3210  df-sn 3672  df-pr 3673  df-op 3675  df-uni 3889  df-br 4084  df-iota 5278  df-fv 5326  df-ov 6004  df-2 9169  df-3 9170  df-4 9171  df-5 9172  df-6 9173  df-7 9174  df-8 9175

This theorem is referenced by:  6p3e9  9261  6t3e18  9682