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Mirrors > Home > ILE Home > Th. List > 4p4e8 | GIF version |
Description: 4 + 4 = 8. (Contributed by NM, 11-May-2004.) |
Ref | Expression |
---|---|
4p4e8 | ⊢ (4 + 4) = 8 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-4 8749 | . . . 4 ⊢ 4 = (3 + 1) | |
2 | 1 | oveq2i 5753 | . . 3 ⊢ (4 + 4) = (4 + (3 + 1)) |
3 | 4cn 8766 | . . . 4 ⊢ 4 ∈ ℂ | |
4 | 3cn 8763 | . . . 4 ⊢ 3 ∈ ℂ | |
5 | ax-1cn 7681 | . . . 4 ⊢ 1 ∈ ℂ | |
6 | 3, 4, 5 | addassi 7742 | . . 3 ⊢ ((4 + 3) + 1) = (4 + (3 + 1)) |
7 | 2, 6 | eqtr4i 2141 | . 2 ⊢ (4 + 4) = ((4 + 3) + 1) |
8 | df-8 8753 | . . 3 ⊢ 8 = (7 + 1) | |
9 | 4p3e7 8832 | . . . 4 ⊢ (4 + 3) = 7 | |
10 | 9 | oveq1i 5752 | . . 3 ⊢ ((4 + 3) + 1) = (7 + 1) |
11 | 8, 10 | eqtr4i 2141 | . 2 ⊢ 8 = ((4 + 3) + 1) |
12 | 7, 11 | eqtr4i 2141 | 1 ⊢ (4 + 4) = 8 |
Colors of variables: wff set class |
Syntax hints: = wceq 1316 (class class class)co 5742 1c1 7589 + caddc 7591 3c3 8740 4c4 8741 7c7 8744 8c8 8745 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-resscn 7680 ax-1cn 7681 ax-1re 7682 ax-addrcl 7685 ax-addass 7690 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-rex 2399 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-iota 5058 df-fv 5101 df-ov 5745 df-2 8747 df-3 8748 df-4 8749 df-5 8750 df-6 8751 df-7 8752 df-8 8753 |
This theorem is referenced by: 4t2e8 8846 |
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