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Mirrors > Home > ILE Home > Th. List > 6t6e36 | GIF version |
Description: 6 times 6 equals 36. (Contributed by Mario Carneiro, 19-Apr-2015.) (Revised by AV, 6-Sep-2021.) |
Ref | Expression |
---|---|
6t6e36 | ⊢ (6 · 6) = ;36 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 6nn0 9183 | . 2 ⊢ 6 ∈ ℕ0 | |
2 | 5nn0 9182 | . 2 ⊢ 5 ∈ ℕ0 | |
3 | df-6 8968 | . 2 ⊢ 6 = (5 + 1) | |
4 | 6t5e30 9476 | . . 3 ⊢ (6 · 5) = ;30 | |
5 | 3nn0 9180 | . . . 4 ⊢ 3 ∈ ℕ0 | |
6 | 5 | dec0u 9390 | . . 3 ⊢ (;10 · 3) = ;30 |
7 | 4, 6 | eqtr4i 2201 | . 2 ⊢ (6 · 5) = (;10 · 3) |
8 | dfdec10 9373 | . . 3 ⊢ ;36 = ((;10 · 3) + 6) | |
9 | 8 | eqcomi 2181 | . 2 ⊢ ((;10 · 3) + 6) = ;36 |
10 | 1, 2, 3, 7, 9 | 4t3lem 9466 | 1 ⊢ (6 · 6) = ;36 |
Colors of variables: wff set class |
Syntax hints: = wceq 1353 (class class class)co 5869 0cc0 7799 1c1 7800 + caddc 7802 · cmul 7804 3c3 8957 5c5 8959 6c6 8960 ;cdc 9370 |
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 614 ax-in2 615 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-14 2151 ax-ext 2159 ax-sep 4118 ax-pow 4171 ax-pr 4206 ax-setind 4533 ax-cnex 7890 ax-resscn 7891 ax-1cn 7892 ax-1re 7893 ax-icn 7894 ax-addcl 7895 ax-addrcl 7896 ax-mulcl 7897 ax-addcom 7899 ax-mulcom 7900 ax-addass 7901 ax-mulass 7902 ax-distr 7903 ax-i2m1 7904 ax-1rid 7906 ax-0id 7907 ax-rnegex 7908 ax-cnre 7910 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-ral 2460 df-rex 2461 df-reu 2462 df-rab 2464 df-v 2739 df-sbc 2963 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-pw 3576 df-sn 3597 df-pr 3598 df-op 3600 df-uni 3808 df-int 3843 df-br 4001 df-opab 4062 df-id 4290 df-xp 4629 df-rel 4630 df-cnv 4631 df-co 4632 df-dm 4633 df-iota 5174 df-fun 5214 df-fv 5220 df-riota 5825 df-ov 5872 df-oprab 5873 df-mpo 5874 df-sub 8117 df-inn 8906 df-2 8964 df-3 8965 df-4 8966 df-5 8967 df-6 8968 df-7 8969 df-8 8970 df-9 8971 df-n0 9163 df-dec 9371 |
This theorem is referenced by: (None) |
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