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Mirrors > Home > MPE Home > Th. List > 7t5e35 | Structured version Visualization version GIF version |
Description: 7 times 5 equals 35. (Contributed by Mario Carneiro, 19-Apr-2015.) |
Ref | Expression |
---|---|
7t5e35 | ⊢ (7 · 5) = ;35 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 7nn0 11737 | . 2 ⊢ 7 ∈ ℕ0 | |
2 | 4nn0 11734 | . 2 ⊢ 4 ∈ ℕ0 | |
3 | df-5 11512 | . 2 ⊢ 5 = (4 + 1) | |
4 | 7t4e28 12030 | . 2 ⊢ (7 · 4) = ;28 | |
5 | 2nn0 11732 | . . 3 ⊢ 2 ∈ ℕ0 | |
6 | 8nn0 11738 | . . 3 ⊢ 8 ∈ ℕ0 | |
7 | eqid 2780 | . . 3 ⊢ ;28 = ;28 | |
8 | 2p1e3 11595 | . . 3 ⊢ (2 + 1) = 3 | |
9 | 5nn0 11735 | . . 3 ⊢ 5 ∈ ℕ0 | |
10 | 8p7e15 12004 | . . 3 ⊢ (8 + 7) = ;15 | |
11 | 5, 6, 1, 7, 8, 9, 10 | decaddci 11979 | . 2 ⊢ (;28 + 7) = ;35 |
12 | 1, 2, 3, 4, 11 | 4t3lem 12016 | 1 ⊢ (7 · 5) = ;35 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1508 (class class class)co 6982 · cmul 10346 2c2 11501 3c3 11502 4c4 11503 5c5 11504 7c7 11506 8c8 11507 ;cdc 11917 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1759 ax-4 1773 ax-5 1870 ax-6 1929 ax-7 1966 ax-8 2053 ax-9 2060 ax-10 2080 ax-11 2094 ax-12 2107 ax-13 2302 ax-ext 2752 ax-sep 5064 ax-nul 5071 ax-pow 5123 ax-pr 5190 ax-un 7285 ax-resscn 10398 ax-1cn 10399 ax-icn 10400 ax-addcl 10401 ax-addrcl 10402 ax-mulcl 10403 ax-mulrcl 10404 ax-mulcom 10405 ax-addass 10406 ax-mulass 10407 ax-distr 10408 ax-i2m1 10409 ax-1ne0 10410 ax-1rid 10411 ax-rnegex 10412 ax-rrecex 10413 ax-cnre 10414 ax-pre-lttri 10415 ax-pre-lttrn 10416 ax-pre-ltadd 10417 |
This theorem depends on definitions: df-bi 199 df-an 388 df-or 835 df-3or 1070 df-3an 1071 df-tru 1511 df-ex 1744 df-nf 1748 df-sb 2017 df-mo 2551 df-eu 2589 df-clab 2761 df-cleq 2773 df-clel 2848 df-nfc 2920 df-ne 2970 df-nel 3076 df-ral 3095 df-rex 3096 df-reu 3097 df-rab 3099 df-v 3419 df-sbc 3684 df-csb 3789 df-dif 3834 df-un 3836 df-in 3838 df-ss 3845 df-pss 3847 df-nul 4182 df-if 4354 df-pw 4427 df-sn 4445 df-pr 4447 df-tp 4449 df-op 4451 df-uni 4718 df-iun 4799 df-br 4935 df-opab 4997 df-mpt 5014 df-tr 5036 df-id 5316 df-eprel 5321 df-po 5330 df-so 5331 df-fr 5370 df-we 5372 df-xp 5417 df-rel 5418 df-cnv 5419 df-co 5420 df-dm 5421 df-rn 5422 df-res 5423 df-ima 5424 df-pred 5991 df-ord 6037 df-on 6038 df-lim 6039 df-suc 6040 df-iota 6157 df-fun 6195 df-fn 6196 df-f 6197 df-f1 6198 df-fo 6199 df-f1o 6200 df-fv 6201 df-riota 6943 df-ov 6985 df-oprab 6986 df-mpo 6987 df-om 7403 df-wrecs 7756 df-recs 7818 df-rdg 7856 df-er 8095 df-en 8313 df-dom 8314 df-sdom 8315 df-pnf 10482 df-mnf 10483 df-ltxr 10485 df-sub 10678 df-nn 11446 df-2 11509 df-3 11510 df-4 11511 df-5 11512 df-6 11513 df-7 11514 df-8 11515 df-9 11516 df-n0 11714 df-dec 11918 |
This theorem is referenced by: 7t6e42 12032 37prm 16316 317prm 16321 log2ublem3 25243 log2ub 25244 235t711 38650 ex-decpmul 38651 257prm 43126 |
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