Theorem 6p2e8 9389

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 9298	. . . . 5 |- 2 = ( 1 + 1 )
2	1	oveq2i 6063	. . . 4 |- ( 6 + 2 ) = ( 6 + ( 1 + 1 ) )
3		6cn 9321	. . . . 5 |- 6 e. CC
4		ax-1cn 8222	. . . . 5 |- 1 e. CC
5	3, 4, 4	addassi 8284	. . . 4 |- ( ( 6 + 1 ) + 1 ) = ( 6 + ( 1 + 1 ) )
6	2, 5	eqtr4i 2258	. . 3 |- ( 6 + 2 ) = ( ( 6 + 1 ) + 1 )
7		df-7 9303	. . . 4 |- 7 = ( 6 + 1 )
8	7	oveq1i 6062	. . 3 |- ( 7 + 1 ) = ( ( 6 + 1 ) + 1 )
9	6, 8	eqtr4i 2258	. 2 |- ( 6 + 2 ) = ( 7 + 1 )
10		df-8 9304	. 2 |- 8 = ( 7 + 1 )
11	9, 10	eqtr4i 2258	1 |- ( 6 + 2 ) = 8

Syntax hints:   = wceq 1398  (class class class)co 6052   1c1 8130   + caddc 8132   2c2 9290   6c6 9294   7c7 9295   8c8 9296

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 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2216  ax-resscn 8221  ax-1cn 8222  ax-1re 8223  ax-addrcl 8226  ax-addass 8231

This theorem depends on definitions:  df-bi 117  df-3an 1007  df-tru 1401  df-nf 1510  df-sb 1812  df-clab 2221  df-cleq 2227  df-clel 2230  df-nfc 2375  df-rex 2528  df-v 2817  df-un 3217  df-in 3219  df-ss 3226  df-sn 3697  df-pr 3698  df-op 3700  df-uni 3917  df-br 4112  df-iota 5314  df-fv 5362  df-ov 6055  df-2 9298  df-3 9299  df-4 9300  df-5 9301  df-6 9302  df-7 9303  df-8 9304

This theorem is referenced by:  6p3e9  9390  6t3e18  9816