Theorem 6p2e8 9185

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 9094	. . . . 5 ⊢ 2 = (1 + 1)
2	1	oveq2i 5954	. . . 4 ⊢ (6 + 2) = (6 + (1 + 1))
3		6cn 9117	. . . . 5 ⊢ 6 ∈ ℂ
4		ax-1cn 8017	. . . . 5 ⊢ 1 ∈ ℂ
5	3, 4, 4	addassi 8079	. . . 4 ⊢ ((6 + 1) + 1) = (6 + (1 + 1))
6	2, 5	eqtr4i 2228	. . 3 ⊢ (6 + 2) = ((6 + 1) + 1)
7		df-7 9099	. . . 4 ⊢ 7 = (6 + 1)
8	7	oveq1i 5953	. . 3 ⊢ (7 + 1) = ((6 + 1) + 1)
9	6, 8	eqtr4i 2228	. 2 ⊢ (6 + 2) = (7 + 1)
10		df-8 9100	. 2 ⊢ 8 = (7 + 1)
11	9, 10	eqtr4i 2228	1 ⊢ (6 + 2) = 8

Syntax hints:   = wceq 1372  (class class class)co 5943  1c1 7925   + caddc 7927  2c2 9086  6c6 9090  7c7 9091  8c8 9092

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 1469  ax-7 1470  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-8 1526  ax-10 1527  ax-11 1528  ax-i12 1529  ax-bndl 1531  ax-4 1532  ax-17 1548  ax-i9 1552  ax-ial 1556  ax-i5r 1557  ax-ext 2186  ax-resscn 8016  ax-1cn 8017  ax-1re 8018  ax-addrcl 8021  ax-addass 8026

This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1375  df-nf 1483  df-sb 1785  df-clab 2191  df-cleq 2197  df-clel 2200  df-nfc 2336  df-rex 2489  df-v 2773  df-un 3169  df-in 3171  df-ss 3178  df-sn 3638  df-pr 3639  df-op 3641  df-uni 3850  df-br 4044  df-iota 5231  df-fv 5278  df-ov 5946  df-2 9094  df-3 9095  df-4 9096  df-5 9097  df-6 9098  df-7 9099  df-8 9100

This theorem is referenced by:  6p3e9  9186  6t3e18  9607