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Mirrors > Home > ILE Home > Th. List > 3t2e6 | GIF version |
Description: 3 times 2 equals 6. (Contributed by NM, 2-Aug-2004.) |
Ref | Expression |
---|---|
3t2e6 | ⊢ (3 · 2) = 6 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3cn 8763 | . . 3 ⊢ 3 ∈ ℂ | |
2 | 1 | times2i 8819 | . 2 ⊢ (3 · 2) = (3 + 3) |
3 | 3p3e6 8830 | . 2 ⊢ (3 + 3) = 6 | |
4 | 2, 3 | eqtri 2138 | 1 ⊢ (3 · 2) = 6 |
Colors of variables: wff set class |
Syntax hints: = wceq 1316 (class class class)co 5742 + caddc 7591 · cmul 7593 2c2 8739 3c3 8740 6c6 8743 |
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-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-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-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-iota 5058 df-fv 5101 df-ov 5745 df-2 8747 df-3 8748 df-4 8749 df-5 8750 df-6 8751 |
This theorem is referenced by: 3t3e9 8845 8th4div3 8907 halfpm6th 8908 halfthird 9292 fac3 10446 sin01bnd 11391 3lcm2e6woprm 11694 3lcm2e6 11765 sincos6thpi 12850 pigt3 12852 |
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