Theorem 6p2e8 9292

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 9201	. . . . 5 |- 2 = ( 1 + 1 )
2	1	oveq2i 6028	. . . 4 |- ( 6 + 2 ) = ( 6 + ( 1 + 1 ) )
3		6cn 9224	. . . . 5 |- 6 e. CC
4		ax-1cn 8124	. . . . 5 |- 1 e. CC
5	3, 4, 4	addassi 8186	. . . 4 |- ( ( 6 + 1 ) + 1 ) = ( 6 + ( 1 + 1 ) )
6	2, 5	eqtr4i 2255	. . 3 |- ( 6 + 2 ) = ( ( 6 + 1 ) + 1 )
7		df-7 9206	. . . 4 |- 7 = ( 6 + 1 )
8	7	oveq1i 6027	. . 3 |- ( 7 + 1 ) = ( ( 6 + 1 ) + 1 )
9	6, 8	eqtr4i 2255	. 2 |- ( 6 + 2 ) = ( 7 + 1 )
10		df-8 9207	. 2 |- 8 = ( 7 + 1 )
11	9, 10	eqtr4i 2255	1 |- ( 6 + 2 ) = 8

Syntax hints:   = wceq 1397  (class class class)co 6017   1c1 8032   + caddc 8034   2c2 9193   6c6 9197   7c7 9198   8c8 9199

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 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213  ax-resscn 8123  ax-1cn 8124  ax-1re 8125  ax-addrcl 8128  ax-addass 8133

This theorem depends on definitions:  df-bi 117  df-3an 1006  df-tru 1400  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-rex 2516  df-v 2804  df-un 3204  df-in 3206  df-ss 3213  df-sn 3675  df-pr 3676  df-op 3678  df-uni 3894  df-br 4089  df-iota 5286  df-fv 5334  df-ov 6020  df-2 9201  df-3 9202  df-4 9203  df-5 9204  df-6 9205  df-7 9206  df-8 9207

This theorem is referenced by:  6p3e9  9293  6t3e18  9714