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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 8181 | . . 3 ⊢ 3 ∈ ℂ | |
2 | 1 | times2i 8230 | . 2 ⊢ (3 · 2) = (3 + 3) |
3 | 3p3e6 8241 | . 2 ⊢ (3 + 3) = 6 | |
4 | 2, 3 | eqtri 2102 | 1 ⊢ (3 · 2) = 6 |
Colors of variables: wff set class |
Syntax hints: = wceq 1285 (class class class)co 5543 + caddc 7046 · cmul 7048 2c2 8156 3c3 8157 6c6 8160 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2064 ax-resscn 7130 ax-1cn 7131 ax-1re 7132 ax-icn 7133 ax-addcl 7134 ax-addrcl 7135 ax-mulcl 7136 ax-mulcom 7139 ax-addass 7140 ax-mulass 7141 ax-distr 7142 ax-1rid 7145 ax-cnre 7149 |
This theorem depends on definitions: df-bi 115 df-3an 922 df-tru 1288 df-nf 1391 df-sb 1687 df-clab 2069 df-cleq 2075 df-clel 2078 df-nfc 2209 df-ral 2354 df-rex 2355 df-v 2604 df-un 2978 df-in 2980 df-ss 2987 df-sn 3412 df-pr 3413 df-op 3415 df-uni 3610 df-br 3794 df-iota 4897 df-fv 4940 df-ov 5546 df-2 8165 df-3 8166 df-4 8167 df-5 8168 df-6 8169 |
This theorem is referenced by: 3t3e9 8256 8th4div3 8317 halfpm6th 8318 fac3 9756 3lcm2e6woprm 10612 3lcm2e6 10683 |
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