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Mirrors > Home > ILE Home > Th. List > 4t2e8 | GIF version |
Description: 4 times 2 equals 8. (Contributed by NM, 2-Aug-2004.) |
Ref | Expression |
---|---|
4t2e8 | ⊢ (4 · 2) = 8 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 4cn 8973 | . . 3 ⊢ 4 ∈ ℂ | |
2 | 1 | times2i 9026 | . 2 ⊢ (4 · 2) = (4 + 4) |
3 | 4p4e8 9040 | . 2 ⊢ (4 + 4) = 8 | |
4 | 2, 3 | eqtri 2198 | 1 ⊢ (4 · 2) = 8 |
Colors of variables: wff set class |
Syntax hints: = wceq 1353 (class class class)co 5868 + caddc 7792 · cmul 7794 2c2 8946 4c4 8948 8c8 8952 |
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 7881 ax-1cn 7882 ax-1re 7883 ax-icn 7884 ax-addcl 7885 ax-addrcl 7886 ax-mulcl 7887 ax-mulcom 7890 ax-addass 7891 ax-mulass 7892 ax-distr 7893 ax-1rid 7896 ax-cnre 7900 |
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 3597 df-pr 3598 df-op 3600 df-uni 3808 df-br 4001 df-iota 5173 df-fv 5219 df-ov 5871 df-2 8954 df-3 8955 df-4 8956 df-5 8957 df-6 8958 df-7 8959 df-8 8960 |
This theorem is referenced by: 8th4div3 9114 4t3e12 9457 sq4e2t8 10590 cu2 10591 sqoddm1div8 10646 cos2bnd 11739 lgsdir2lem2 14063 ex-exp 14101 |
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