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Mirrors > Home > ILE Home > Th. List > 6p4e10 | GIF version |
Description: 6 + 4 = 10. (Contributed by NM, 5-Feb-2007.) |
Ref | Expression |
---|---|
6p4e10 | ⊢ (6 + 4) = 10 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-4 7755 | . . . 4 ⊢ 4 = (3 + 1) | |
2 | 1 | oveq2i 5466 | . . 3 ⊢ (6 + 4) = (6 + (3 + 1)) |
3 | 6cn 7777 | . . . 4 ⊢ 6 ∈ ℂ | |
4 | 3cn 7770 | . . . 4 ⊢ 3 ∈ ℂ | |
5 | ax-1cn 6776 | . . . 4 ⊢ 1 ∈ ℂ | |
6 | 3, 4, 5 | addassi 6833 | . . 3 ⊢ ((6 + 3) + 1) = (6 + (3 + 1)) |
7 | 2, 6 | eqtr4i 2060 | . 2 ⊢ (6 + 4) = ((6 + 3) + 1) |
8 | df-10 7761 | . . 3 ⊢ 10 = (9 + 1) | |
9 | 6p3e9 7840 | . . . 4 ⊢ (6 + 3) = 9 | |
10 | 9 | oveq1i 5465 | . . 3 ⊢ ((6 + 3) + 1) = (9 + 1) |
11 | 8, 10 | eqtr4i 2060 | . 2 ⊢ 10 = ((6 + 3) + 1) |
12 | 7, 11 | eqtr4i 2060 | 1 ⊢ (6 + 4) = 10 |
Colors of variables: wff set class |
Syntax hints: = wceq 1242 (class class class)co 5455 1c1 6712 + caddc 6714 3c3 7745 4c4 7746 6c6 7748 9c9 7751 10c10 7752 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 ax-resscn 6775 ax-1cn 6776 ax-1re 6777 ax-addrcl 6780 ax-addass 6785 |
This theorem depends on definitions: df-bi 110 df-3an 886 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-rex 2306 df-v 2553 df-un 2916 df-in 2918 df-ss 2925 df-sn 3373 df-pr 3374 df-op 3376 df-uni 3572 df-br 3756 df-iota 4810 df-fv 4853 df-ov 5458 df-2 7753 df-3 7754 df-4 7755 df-5 7756 df-6 7757 df-7 7758 df-8 7759 df-9 7760 df-10 7761 |
This theorem is referenced by: 6p5e11 8193 6t5e30 8223 |
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