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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 8483 | . . . 4 ⊢ 4 = (3 + 1) | |
2 | 1 | oveq2i 5663 | . . 3 ⊢ (4 + 4) = (4 + (3 + 1)) |
3 | 4cn 8500 | . . . 4 ⊢ 4 ∈ ℂ | |
4 | 3cn 8497 | . . . 4 ⊢ 3 ∈ ℂ | |
5 | ax-1cn 7438 | . . . 4 ⊢ 1 ∈ ℂ | |
6 | 3, 4, 5 | addassi 7496 | . . 3 ⊢ ((4 + 3) + 1) = (4 + (3 + 1)) |
7 | 2, 6 | eqtr4i 2111 | . 2 ⊢ (4 + 4) = ((4 + 3) + 1) |
8 | df-8 8487 | . . 3 ⊢ 8 = (7 + 1) | |
9 | 4p3e7 8560 | . . . 4 ⊢ (4 + 3) = 7 | |
10 | 9 | oveq1i 5662 | . . 3 ⊢ ((4 + 3) + 1) = (7 + 1) |
11 | 8, 10 | eqtr4i 2111 | . 2 ⊢ 8 = ((4 + 3) + 1) |
12 | 7, 11 | eqtr4i 2111 | 1 ⊢ (4 + 4) = 8 |
Colors of variables: wff set class |
Syntax hints: = wceq 1289 (class class class)co 5652 1c1 7351 + caddc 7353 3c3 8474 4c4 8475 7c7 8478 8c8 8479 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 ax-resscn 7437 ax-1cn 7438 ax-1re 7439 ax-addrcl 7442 ax-addass 7447 |
This theorem depends on definitions: df-bi 115 df-3an 926 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-rex 2365 df-v 2621 df-un 3003 df-in 3005 df-ss 3012 df-sn 3452 df-pr 3453 df-op 3455 df-uni 3654 df-br 3846 df-iota 4980 df-fv 5023 df-ov 5655 df-2 8481 df-3 8482 df-4 8483 df-5 8484 df-6 8485 df-7 8486 df-8 8487 |
This theorem is referenced by: 4t2e8 8574 |
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