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Mirrors > Home > ILE Home > Th. List > 6p4e10 | GIF version |
Description: 6 + 4 = 10. (Contributed by NM, 5-Feb-2007.) (Revised by Stanislas Polu, 7-Apr-2020.) (Revised by AV, 6-Sep-2021.) |
Ref | Expression |
---|---|
6p4e10 | ⊢ (6 + 4) = ;10 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-4 8749 | . . . 4 ⊢ 4 = (3 + 1) | |
2 | 1 | oveq2i 5753 | . . 3 ⊢ (6 + 4) = (6 + (3 + 1)) |
3 | 6cn 8770 | . . . 4 ⊢ 6 ∈ ℂ | |
4 | 3cn 8763 | . . . 4 ⊢ 3 ∈ ℂ | |
5 | ax-1cn 7681 | . . . 4 ⊢ 1 ∈ ℂ | |
6 | 3, 4, 5 | addassi 7742 | . . 3 ⊢ ((6 + 3) + 1) = (6 + (3 + 1)) |
7 | 2, 6 | eqtr4i 2141 | . 2 ⊢ (6 + 4) = ((6 + 3) + 1) |
8 | 6p3e9 8838 | . . 3 ⊢ (6 + 3) = 9 | |
9 | 8 | oveq1i 5752 | . 2 ⊢ ((6 + 3) + 1) = (9 + 1) |
10 | 9p1e10 9152 | . 2 ⊢ (9 + 1) = ;10 | |
11 | 7, 9, 10 | 3eqtri 2142 | 1 ⊢ (6 + 4) = ;10 |
Colors of variables: wff set class |
Syntax hints: = wceq 1316 (class class class)co 5742 0cc0 7588 1c1 7589 + caddc 7591 3c3 8740 4c4 8741 6c6 8743 9c9 8746 ;cdc 9150 |
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-sep 4016 ax-cnex 7679 ax-resscn 7680 ax-1cn 7681 ax-1re 7682 ax-icn 7683 ax-addcl 7684 ax-addrcl 7685 ax-mulcl 7686 ax-mulcom 7689 ax-addass 7690 ax-mulass 7691 ax-distr 7692 ax-1rid 7695 ax-0id 7696 ax-cnre 7699 |
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-ral 2398 df-rex 2399 df-rab 2402 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-int 3742 df-br 3900 df-iota 5058 df-fv 5101 df-ov 5745 df-inn 8689 df-2 8747 df-3 8748 df-4 8749 df-5 8750 df-6 8751 df-7 8752 df-8 8753 df-9 8754 df-dec 9151 |
This theorem is referenced by: 6p5e11 9222 6t5e30 9256 ex-bc 12868 |
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