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Mirrors > Home > ILE Home > Th. List > 8t5e40 | GIF version |
Description: 8 times 5 equals 40. (Contributed by Mario Carneiro, 19-Apr-2015.) (Revised by AV, 6-Sep-2021.) |
Ref | Expression |
---|---|
8t5e40 | ⊢ (8 · 5) = ;40 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 8nn0 9114 | . 2 ⊢ 8 ∈ ℕ0 | |
2 | 4nn0 9110 | . 2 ⊢ 4 ∈ ℕ0 | |
3 | df-5 8896 | . 2 ⊢ 5 = (4 + 1) | |
4 | 8t4e32 9412 | . 2 ⊢ (8 · 4) = ;32 | |
5 | 3nn0 9109 | . . 3 ⊢ 3 ∈ ℕ0 | |
6 | 2nn0 9108 | . . 3 ⊢ 2 ∈ ℕ0 | |
7 | eqid 2157 | . . 3 ⊢ ;32 = ;32 | |
8 | 3p1e4 8969 | . . 3 ⊢ (3 + 1) = 4 | |
9 | 8cn 8920 | . . . 4 ⊢ 8 ∈ ℂ | |
10 | 2cn 8905 | . . . 4 ⊢ 2 ∈ ℂ | |
11 | 8p2e10 9375 | . . . 4 ⊢ (8 + 2) = ;10 | |
12 | 9, 10, 11 | addcomli 8021 | . . 3 ⊢ (2 + 8) = ;10 |
13 | 5, 6, 1, 7, 8, 12 | decaddci2 9357 | . 2 ⊢ (;32 + 8) = ;40 |
14 | 1, 2, 3, 4, 13 | 4t3lem 9392 | 1 ⊢ (8 · 5) = ;40 |
Colors of variables: wff set class |
Syntax hints: = wceq 1335 (class class class)co 5825 0cc0 7733 1c1 7734 · cmul 7738 2c2 8885 3c3 8886 4c4 8887 5c5 8888 8c8 8891 ;cdc 9296 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4083 ax-pow 4136 ax-pr 4170 ax-setind 4497 ax-cnex 7824 ax-resscn 7825 ax-1cn 7826 ax-1re 7827 ax-icn 7828 ax-addcl 7829 ax-addrcl 7830 ax-mulcl 7831 ax-addcom 7833 ax-mulcom 7834 ax-addass 7835 ax-mulass 7836 ax-distr 7837 ax-i2m1 7838 ax-1rid 7840 ax-0id 7841 ax-rnegex 7842 ax-cnre 7844 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-fal 1341 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ne 2328 df-ral 2440 df-rex 2441 df-reu 2442 df-rab 2444 df-v 2714 df-sbc 2938 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3774 df-int 3809 df-br 3967 df-opab 4027 df-id 4254 df-xp 4593 df-rel 4594 df-cnv 4595 df-co 4596 df-dm 4597 df-iota 5136 df-fun 5173 df-fv 5179 df-riota 5781 df-ov 5828 df-oprab 5829 df-mpo 5830 df-sub 8049 df-inn 8835 df-2 8893 df-3 8894 df-4 8895 df-5 8896 df-6 8897 df-7 8898 df-8 8899 df-9 8900 df-n0 9092 df-dec 9297 |
This theorem is referenced by: 8t6e48 9414 |
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