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Mirrors > Home > ILE Home > Th. List > 6p3e9 | GIF version |
Description: 6 + 3 = 9. (Contributed by NM, 11-May-2004.) |
Ref | Expression |
---|---|
6p3e9 | ⊢ (6 + 3) = 9 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3 8543 | . . . 4 ⊢ 3 = (2 + 1) | |
2 | 1 | oveq2i 5677 | . . 3 ⊢ (6 + 3) = (6 + (2 + 1)) |
3 | 6cn 8565 | . . . 4 ⊢ 6 ∈ ℂ | |
4 | 2cn 8554 | . . . 4 ⊢ 2 ∈ ℂ | |
5 | ax-1cn 7499 | . . . 4 ⊢ 1 ∈ ℂ | |
6 | 3, 4, 5 | addassi 7557 | . . 3 ⊢ ((6 + 2) + 1) = (6 + (2 + 1)) |
7 | 2, 6 | eqtr4i 2112 | . 2 ⊢ (6 + 3) = ((6 + 2) + 1) |
8 | df-9 8549 | . . 3 ⊢ 9 = (8 + 1) | |
9 | 6p2e8 8626 | . . . 4 ⊢ (6 + 2) = 8 | |
10 | 9 | oveq1i 5676 | . . 3 ⊢ ((6 + 2) + 1) = (8 + 1) |
11 | 8, 10 | eqtr4i 2112 | . 2 ⊢ 9 = ((6 + 2) + 1) |
12 | 7, 11 | eqtr4i 2112 | 1 ⊢ (6 + 3) = 9 |
Colors of variables: wff set class |
Syntax hints: = wceq 1290 (class class class)co 5666 1c1 7412 + caddc 7414 2c2 8534 3c3 8535 6c6 8538 8c8 8540 9c9 8541 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 ax-resscn 7498 ax-1cn 7499 ax-1re 7500 ax-addrcl 7503 ax-addass 7508 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-rex 2366 df-v 2622 df-un 3004 df-in 3006 df-ss 3013 df-sn 3456 df-pr 3457 df-op 3459 df-uni 3660 df-br 3852 df-iota 4993 df-fv 5036 df-ov 5669 df-2 8542 df-3 8543 df-4 8544 df-5 8545 df-6 8546 df-7 8547 df-8 8548 df-9 8549 |
This theorem is referenced by: 3t3e9 8634 6p4e10 9009 ex-gcd 11931 |
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