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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 7974 | . . . 4 ⊢ 3 = (2 + 1) | |
2 | 1 | oveq2i 5523 | . . 3 ⊢ (6 + 3) = (6 + (2 + 1)) |
3 | 6cn 7997 | . . . 4 ⊢ 6 ∈ ℂ | |
4 | 2cn 7986 | . . . 4 ⊢ 2 ∈ ℂ | |
5 | ax-1cn 6977 | . . . 4 ⊢ 1 ∈ ℂ | |
6 | 3, 4, 5 | addassi 7035 | . . 3 ⊢ ((6 + 2) + 1) = (6 + (2 + 1)) |
7 | 2, 6 | eqtr4i 2063 | . 2 ⊢ (6 + 3) = ((6 + 2) + 1) |
8 | df-9 7980 | . . 3 ⊢ 9 = (8 + 1) | |
9 | 6p2e8 8061 | . . . 4 ⊢ (6 + 2) = 8 | |
10 | 9 | oveq1i 5522 | . . 3 ⊢ ((6 + 2) + 1) = (8 + 1) |
11 | 8, 10 | eqtr4i 2063 | . 2 ⊢ 9 = ((6 + 2) + 1) |
12 | 7, 11 | eqtr4i 2063 | 1 ⊢ (6 + 3) = 9 |
Colors of variables: wff set class |
Syntax hints: = wceq 1243 (class class class)co 5512 1c1 6890 + caddc 6892 2c2 7964 3c3 7965 6c6 7968 8c8 7970 9c9 7971 |
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 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-resscn 6976 ax-1cn 6977 ax-1re 6978 ax-addrcl 6981 ax-addass 6986 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rex 2312 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-br 3765 df-iota 4867 df-fv 4910 df-ov 5515 df-2 7973 df-3 7974 df-4 7975 df-5 7976 df-6 7977 df-7 7978 df-8 7979 df-9 7980 |
This theorem is referenced by: 6p4e10 8063 3t3e9 8072 |
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