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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 8982 | . . . 4 ⊢ 3 = (2 + 1) | |
2 | 1 | oveq2i 5889 | . . 3 ⊢ (6 + 3) = (6 + (2 + 1)) |
3 | 6cn 9004 | . . . 4 ⊢ 6 ∈ ℂ | |
4 | 2cn 8993 | . . . 4 ⊢ 2 ∈ ℂ | |
5 | ax-1cn 7907 | . . . 4 ⊢ 1 ∈ ℂ | |
6 | 3, 4, 5 | addassi 7968 | . . 3 ⊢ ((6 + 2) + 1) = (6 + (2 + 1)) |
7 | 2, 6 | eqtr4i 2201 | . 2 ⊢ (6 + 3) = ((6 + 2) + 1) |
8 | df-9 8988 | . . 3 ⊢ 9 = (8 + 1) | |
9 | 6p2e8 9071 | . . . 4 ⊢ (6 + 2) = 8 | |
10 | 9 | oveq1i 5888 | . . 3 ⊢ ((6 + 2) + 1) = (8 + 1) |
11 | 8, 10 | eqtr4i 2201 | . 2 ⊢ 9 = ((6 + 2) + 1) |
12 | 7, 11 | eqtr4i 2201 | 1 ⊢ (6 + 3) = 9 |
Colors of variables: wff set class |
Syntax hints: = wceq 1353 (class class class)co 5878 1c1 7815 + caddc 7817 2c2 8973 3c3 8974 6c6 8977 8c8 8979 9c9 8980 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 ax-resscn 7906 ax-1cn 7907 ax-1re 7908 ax-addrcl 7911 ax-addass 7916 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-rex 2461 df-v 2741 df-un 3135 df-in 3137 df-ss 3144 df-sn 3600 df-pr 3601 df-op 3603 df-uni 3812 df-br 4006 df-iota 5180 df-fv 5226 df-ov 5881 df-2 8981 df-3 8982 df-4 8983 df-5 8984 df-6 8985 df-7 8986 df-8 8987 df-9 8988 |
This theorem is referenced by: 3t3e9 9079 6p4e10 9458 ex-gcd 14623 |
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