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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 8988 | . . 3 ⊢ 2 ∈ ℂ | |
2 | 1 | 2timesi 9047 | . 2 ⊢ (2 · 2) = (2 + 2) |
3 | 2p2e4 9044 | . 2 ⊢ (2 + 2) = 4 | |
4 | 2, 3 | eqtri 2198 | 1 ⊢ (2 · 2) = 4 |
Colors of variables: wff set class |
Syntax hints: = wceq 1353 (class class class)co 5874 + caddc 7813 · cmul 7815 2c2 8968 4c4 8970 |
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 7902 ax-1cn 7903 ax-1re 7904 ax-icn 7905 ax-addcl 7906 ax-addrcl 7907 ax-mulcl 7908 ax-mulcom 7911 ax-addass 7912 ax-mulass 7913 ax-distr 7914 ax-1rid 7917 ax-cnre 7921 |
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 2739 df-un 3133 df-in 3135 df-ss 3142 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-br 4004 df-iota 5178 df-fv 5224 df-ov 5877 df-2 8976 df-3 8977 df-4 8978 |
This theorem is referenced by: 4d2e2 9077 halfpm6th 9137 div4p1lem1div2 9170 3halfnz 9348 decbin0 9521 sq2 10612 sq4e2t8 10614 sqoddm1div8 10670 faclbnd2 10717 4bc2eq6 10749 amgm2 11122 sin4lt0 11769 z4even 11915 flodddiv4 11933 flodddiv4t2lthalf 11936 4nprm 12123 dveflem 14080 sin0pilem2 14096 sinhalfpilem 14105 sincosq1lem 14139 tangtx 14152 sincos4thpi 14154 ex-fl 14359 |
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