Theorem 6p2e8 9131

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 9041	. . . . 5 |- 2 = ( 1 + 1 )
2	1	oveq2i 5929	. . . 4 |- ( 6 + 2 ) = ( 6 + ( 1 + 1 ) )
3		6cn 9064	. . . . 5 |- 6 e. CC
4		ax-1cn 7965	. . . . 5 |- 1 e. CC
5	3, 4, 4	addassi 8027	. . . 4 |- ( ( 6 + 1 ) + 1 ) = ( 6 + ( 1 + 1 ) )
6	2, 5	eqtr4i 2217	. . 3 |- ( 6 + 2 ) = ( ( 6 + 1 ) + 1 )
7		df-7 9046	. . . 4 |- 7 = ( 6 + 1 )
8	7	oveq1i 5928	. . 3 |- ( 7 + 1 ) = ( ( 6 + 1 ) + 1 )
9	6, 8	eqtr4i 2217	. 2 |- ( 6 + 2 ) = ( 7 + 1 )
10		df-8 9047	. 2 |- 8 = ( 7 + 1 )
11	9, 10	eqtr4i 2217	1 |- ( 6 + 2 ) = 8

Syntax hints:   = wceq 1364  (class class class)co 5918   1c1 7873   + caddc 7875   2c2 9033   6c6 9037   7c7 9038   8c8 9039

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 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175  ax-resscn 7964  ax-1cn 7965  ax-1re 7966  ax-addrcl 7969  ax-addass 7974

This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-rex 2478  df-v 2762  df-un 3157  df-in 3159  df-ss 3166  df-sn 3624  df-pr 3625  df-op 3627  df-uni 3836  df-br 4030  df-iota 5215  df-fv 5262  df-ov 5921  df-2 9041  df-3 9042  df-4 9043  df-5 9044  df-6 9045  df-7 9046  df-8 9047

This theorem is referenced by:  6p3e9  9132  6t3e18  9552