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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 8997 | . . 3 ⊢ 3 ∈ ℂ | |
2 | 1 | times2i 9053 | . 2 ⊢ (3 · 2) = (3 + 3) |
3 | 3p3e6 9064 | . 2 ⊢ (3 + 3) = 6 | |
4 | 2, 3 | eqtri 2198 | 1 ⊢ (3 · 2) = 6 |
Colors of variables: wff set class |
Syntax hints: = wceq 1353 (class class class)co 5878 + caddc 7817 · cmul 7819 2c2 8973 3c3 8974 6c6 8977 |
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-icn 7909 ax-addcl 7910 ax-addrcl 7911 ax-mulcl 7912 ax-mulcom 7915 ax-addass 7916 ax-mulass 7917 ax-distr 7918 ax-1rid 7921 ax-cnre 7925 |
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-ral 2460 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 |
This theorem is referenced by: 3t3e9 9079 8th4div3 9141 halfpm6th 9142 halfthird 9529 fac3 10715 sin01bnd 11768 3lcm2e6woprm 12089 3lcm2e6 12163 sincos6thpi 14424 pigt3 14426 2lgsoddprmlem3d 14619 |
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