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Mirrors > Home > ILE Home > Th. List > 3p3e6 | Unicode version |
Description: 3 + 3 = 6. (Contributed by NM, 11-May-2004.) |
Ref | Expression |
---|---|
3p3e6 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3 8888 | . . . 4 | |
2 | 1 | oveq2i 5832 | . . 3 |
3 | 3cn 8903 | . . . 4 | |
4 | 2cn 8899 | . . . 4 | |
5 | ax-1cn 7820 | . . . 4 | |
6 | 3, 4, 5 | addassi 7881 | . . 3 |
7 | 2, 6 | eqtr4i 2181 | . 2 |
8 | df-6 8891 | . . 3 | |
9 | 3p2e5 8969 | . . . 4 | |
10 | 9 | oveq1i 5831 | . . 3 |
11 | 8, 10 | eqtr4i 2181 | . 2 |
12 | 7, 11 | eqtr4i 2181 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1335 (class class class)co 5821 c1 7728 caddc 7730 c2 8879 c3 8880 c5 8882 c6 8883 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 ax-resscn 7819 ax-1cn 7820 ax-1re 7821 ax-addrcl 7824 ax-addass 7829 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-rex 2441 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3773 df-br 3966 df-iota 5134 df-fv 5177 df-ov 5824 df-2 8887 df-3 8888 df-4 8889 df-5 8890 df-6 8891 |
This theorem is referenced by: 3t2e6 8984 binom4 13283 ex-dvds 13293 ex-gcd 13294 |
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