Theorem 6p2e8 9256

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 9165	. . . . 5 ⊢ 2 = (1 + 1)
2	1	oveq2i 6011	. . . 4 ⊢ (6 + 2) = (6 + (1 + 1))
3		6cn 9188	. . . . 5 ⊢ 6 ∈ ℂ
4		ax-1cn 8088	. . . . 5 ⊢ 1 ∈ ℂ
5	3, 4, 4	addassi 8150	. . . 4 ⊢ ((6 + 1) + 1) = (6 + (1 + 1))
6	2, 5	eqtr4i 2253	. . 3 ⊢ (6 + 2) = ((6 + 1) + 1)
7		df-7 9170	. . . 4 ⊢ 7 = (6 + 1)
8	7	oveq1i 6010	. . 3 ⊢ (7 + 1) = ((6 + 1) + 1)
9	6, 8	eqtr4i 2253	. 2 ⊢ (6 + 2) = (7 + 1)
10		df-8 9171	. 2 ⊢ 8 = (7 + 1)
11	9, 10	eqtr4i 2253	1 ⊢ (6 + 2) = 8

Syntax hints:   = wceq 1395  (class class class)co 6000  1c1 7996   + caddc 7998  2c2 9157  6c6 9161  7c7 9162  8c8 9163

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 8087  ax-1cn 8088  ax-1re 8089  ax-addrcl 8092  ax-addass 8097

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 3888  df-br 4083  df-iota 5277  df-fv 5325  df-ov 6003  df-2 9165  df-3 9166  df-4 9167  df-5 9168  df-6 9169  df-7 9170  df-8 9171

This theorem is referenced by:  6p3e9  9257  6t3e18  9678