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Mirrors > Home > ILE Home > Th. List > 6t2e12 | GIF version |
Description: 6 times 2 equals 12. (Contributed by Mario Carneiro, 19-Apr-2015.) |
Ref | Expression |
---|---|
6t2e12 | ⊢ (6 · 2) = ;12 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 6cn 9030 | . . 3 ⊢ 6 ∈ ℂ | |
2 | 1 | times2i 9079 | . 2 ⊢ (6 · 2) = (6 + 6) |
3 | 6p6e12 9486 | . 2 ⊢ (6 + 6) = ;12 | |
4 | 2, 3 | eqtri 2210 | 1 ⊢ (6 · 2) = ;12 |
Colors of variables: wff set class |
Syntax hints: = wceq 1364 (class class class)co 5895 1c1 7841 + caddc 7843 · cmul 7845 2c2 8999 6c6 9003 ;cdc 9413 |
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-in1 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4192 ax-pr 4227 ax-setind 4554 ax-cnex 7931 ax-resscn 7932 ax-1cn 7933 ax-1re 7934 ax-icn 7935 ax-addcl 7936 ax-addrcl 7937 ax-mulcl 7938 ax-addcom 7940 ax-mulcom 7941 ax-addass 7942 ax-mulass 7943 ax-distr 7944 ax-i2m1 7945 ax-1rid 7947 ax-0id 7948 ax-rnegex 7949 ax-cnre 7951 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-fal 1370 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ne 2361 df-ral 2473 df-rex 2474 df-reu 2475 df-rab 2477 df-v 2754 df-sbc 2978 df-dif 3146 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-int 3860 df-br 4019 df-opab 4080 df-id 4311 df-xp 4650 df-rel 4651 df-cnv 4652 df-co 4653 df-dm 4654 df-iota 5196 df-fun 5237 df-fv 5243 df-riota 5851 df-ov 5898 df-oprab 5899 df-mpo 5900 df-sub 8159 df-inn 8949 df-2 9007 df-3 9008 df-4 9009 df-5 9010 df-6 9011 df-7 9012 df-8 9013 df-9 9014 df-n0 9206 df-dec 9414 |
This theorem is referenced by: 6t3e18 9517 6lcm4e12 12118 |
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