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Mirrors > Home > MPE Home > Th. List > 8t7e56 | Structured version Visualization version GIF version |
Description: 8 times 7 equals 56. (Contributed by Mario Carneiro, 19-Apr-2015.) |
Ref | Expression |
---|---|
8t7e56 | ⊢ (8 · 7) = ;56 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 8nn0 12491 | . 2 ⊢ 8 ∈ ℕ0 | |
2 | 6nn0 12489 | . 2 ⊢ 6 ∈ ℕ0 | |
3 | df-7 12276 | . 2 ⊢ 7 = (6 + 1) | |
4 | 8t6e48 12792 | . 2 ⊢ (8 · 6) = ;48 | |
5 | 4nn0 12487 | . . 3 ⊢ 4 ∈ ℕ0 | |
6 | eqid 2733 | . . 3 ⊢ ;48 = ;48 | |
7 | 4p1e5 12354 | . . 3 ⊢ (4 + 1) = 5 | |
8 | 8p8e16 12759 | . . 3 ⊢ (8 + 8) = ;16 | |
9 | 5, 1, 1, 6, 7, 2, 8 | decaddci 12734 | . 2 ⊢ (;48 + 8) = ;56 |
10 | 1, 2, 3, 4, 9 | 4t3lem 12770 | 1 ⊢ (8 · 7) = ;56 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1542 (class class class)co 7404 · cmul 11111 4c4 12265 5c5 12266 6c6 12267 7c7 12268 8c8 12269 ;cdc 12673 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-10 2138 ax-11 2155 ax-12 2172 ax-ext 2704 ax-sep 5298 ax-nul 5305 ax-pow 5362 ax-pr 5426 ax-un 7720 ax-resscn 11163 ax-1cn 11164 ax-icn 11165 ax-addcl 11166 ax-addrcl 11167 ax-mulcl 11168 ax-mulrcl 11169 ax-mulcom 11170 ax-addass 11171 ax-mulass 11172 ax-distr 11173 ax-i2m1 11174 ax-1ne0 11175 ax-1rid 11176 ax-rnegex 11177 ax-rrecex 11178 ax-cnre 11179 ax-pre-lttri 11180 ax-pre-lttrn 11181 ax-pre-ltadd 11182 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-3or 1089 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-nf 1787 df-sb 2069 df-mo 2535 df-eu 2564 df-clab 2711 df-cleq 2725 df-clel 2811 df-nfc 2886 df-ne 2942 df-nel 3048 df-ral 3063 df-rex 3072 df-reu 3378 df-rab 3434 df-v 3477 df-sbc 3777 df-csb 3893 df-dif 3950 df-un 3952 df-in 3954 df-ss 3964 df-pss 3966 df-nul 4322 df-if 4528 df-pw 4603 df-sn 4628 df-pr 4630 df-op 4634 df-uni 4908 df-iun 4998 df-br 5148 df-opab 5210 df-mpt 5231 df-tr 5265 df-id 5573 df-eprel 5579 df-po 5587 df-so 5588 df-fr 5630 df-we 5632 df-xp 5681 df-rel 5682 df-cnv 5683 df-co 5684 df-dm 5685 df-rn 5686 df-res 5687 df-ima 5688 df-pred 6297 df-ord 6364 df-on 6365 df-lim 6366 df-suc 6367 df-iota 6492 df-fun 6542 df-fn 6543 df-f 6544 df-f1 6545 df-fo 6546 df-f1o 6547 df-fv 6548 df-riota 7360 df-ov 7407 df-oprab 7408 df-mpo 7409 df-om 7851 df-2nd 7971 df-frecs 8261 df-wrecs 8292 df-recs 8366 df-rdg 8405 df-er 8699 df-en 8936 df-dom 8937 df-sdom 8938 df-pnf 11246 df-mnf 11247 df-ltxr 11249 df-sub 11442 df-nn 12209 df-2 12271 df-3 12272 df-4 12273 df-5 12274 df-6 12275 df-7 12276 df-8 12277 df-9 12278 df-n0 12469 df-dec 12674 |
This theorem is referenced by: 8t8e64 12794 139prm 17053 317prm 17055 hgt750lem2 33602 139prmALT 46199 127prm 46202 |
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