Theorem 4p4e8 9432

Description: 4 + 4 = 8. (Contributed by NM, 11-May-2004.)

Assertion

Ref	Expression
4p4e8	⊢ (4 + 4) = 8

Proof of Theorem 4p4e8

Step	Hyp	Ref	Expression
1		df-4 9347	. . . 4 ⊢ 4 = (3 + 1)
2	1	oveq2i 6089	. . 3 ⊢ (4 + 4) = (4 + (3 + 1))
3		4cn 9364	. . . 4 ⊢ 4 ∈ ℂ
4		3cn 9361	. . . 4 ⊢ 3 ∈ ℂ
5		ax-1cn 8265	. . . 4 ⊢ 1 ∈ ℂ
6	3, 4, 5	addassi 8327	. . 3 ⊢ ((4 + 3) + 1) = (4 + (3 + 1))
7	2, 6	eqtr4i 2262	. 2 ⊢ (4 + 4) = ((4 + 3) + 1)
8		df-8 9351	. . 3 ⊢ 8 = (7 + 1)
9		4p3e7 9431	. . . 4 ⊢ (4 + 3) = 7
10	9	oveq1i 6088	. . 3 ⊢ ((4 + 3) + 1) = (7 + 1)
11	8, 10	eqtr4i 2262	. 2 ⊢ 8 = ((4 + 3) + 1)
12	7, 11	eqtr4i 2262	1 ⊢ (4 + 4) = 8

Syntax hints:   = wceq 1402  (class class class)co 6078  1c1 8173   + caddc 8175  3c3 9338  4c4 9339  7c7 9342  8c8 9343

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 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220  ax-resscn 8264  ax-1cn 8265  ax-1re 8266  ax-addrcl 8269  ax-addass 8274

This theorem depends on definitions:  df-bi 117  df-3an 1011  df-tru 1405  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-rex 2534  df-v 2823  df-un 3224  df-in 3226  df-ss 3233  df-sn 3714  df-pr 3715  df-op 3717  df-uni 3934  df-br 4129  df-iota 5335  df-fv 5383  df-ov 6081  df-2 9345  df-3 9346  df-4 9347  df-5 9348  df-6 9349  df-7 9350  df-8 9351

This theorem is referenced by:  4t2e8  9445