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Mirrors > Home > ILE Home > Th. List > 2t2e4 | GIF version |
Description: 2 times 2 equals 4. (Contributed by NM, 1-Aug-1999.) |
Ref | Expression |
---|---|
2t2e4 | ⊢ (2 · 2) = 4 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2cn 8949 | . . 3 ⊢ 2 ∈ ℂ | |
2 | 1 | 2timesi 9008 | . 2 ⊢ (2 · 2) = (2 + 2) |
3 | 2p2e4 9005 | . 2 ⊢ (2 + 2) = 4 | |
4 | 2, 3 | eqtri 2191 | 1 ⊢ (2 · 2) = 4 |
Colors of variables: wff set class |
Syntax hints: = wceq 1348 (class class class)co 5853 + caddc 7777 · cmul 7779 2c2 8929 4c4 8931 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 ax-resscn 7866 ax-1cn 7867 ax-1re 7868 ax-icn 7869 ax-addcl 7870 ax-addrcl 7871 ax-mulcl 7872 ax-mulcom 7875 ax-addass 7876 ax-mulass 7877 ax-distr 7878 ax-1rid 7881 ax-cnre 7885 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-sn 3589 df-pr 3590 df-op 3592 df-uni 3797 df-br 3990 df-iota 5160 df-fv 5206 df-ov 5856 df-2 8937 df-3 8938 df-4 8939 |
This theorem is referenced by: 4d2e2 9038 halfpm6th 9098 div4p1lem1div2 9131 3halfnz 9309 decbin0 9482 sq2 10571 sq4e2t8 10573 sqoddm1div8 10629 faclbnd2 10676 4bc2eq6 10708 amgm2 11082 sin4lt0 11729 z4even 11875 flodddiv4 11893 flodddiv4t2lthalf 11896 4nprm 12083 dveflem 13481 sin0pilem2 13497 sinhalfpilem 13506 sincosq1lem 13540 tangtx 13553 sincos4thpi 13555 ex-fl 13760 |
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