![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > 8t8e64 | GIF version |
Description: 8 times 8 equals 64. (Contributed by Mario Carneiro, 19-Apr-2015.) |
Ref | Expression |
---|---|
8t8e64 | ⊢ (8 · 8) = ;64 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 8nn0 8897 | . 2 ⊢ 8 ∈ ℕ0 | |
2 | 7nn0 8896 | . 2 ⊢ 7 ∈ ℕ0 | |
3 | df-8 8688 | . 2 ⊢ 8 = (7 + 1) | |
4 | 8t7e56 9198 | . 2 ⊢ (8 · 7) = ;56 | |
5 | 5nn0 8894 | . . 3 ⊢ 5 ∈ ℕ0 | |
6 | 6nn0 8895 | . . 3 ⊢ 6 ∈ ℕ0 | |
7 | eqid 2113 | . . 3 ⊢ ;56 = ;56 | |
8 | 5p1e6 8754 | . . 3 ⊢ (5 + 1) = 6 | |
9 | 4nn0 8893 | . . 3 ⊢ 4 ∈ ℕ0 | |
10 | 1 | nn0cni 8886 | . . . 4 ⊢ 8 ∈ ℂ |
11 | 6 | nn0cni 8886 | . . . 4 ⊢ 6 ∈ ℂ |
12 | 8p6e14 9162 | . . . 4 ⊢ (8 + 6) = ;14 | |
13 | 10, 11, 12 | addcomli 7823 | . . 3 ⊢ (6 + 8) = ;14 |
14 | 5, 6, 1, 7, 8, 9, 13 | decaddci 9139 | . 2 ⊢ (;56 + 8) = ;64 |
15 | 1, 2, 3, 4, 14 | 4t3lem 9175 | 1 ⊢ (8 · 8) = ;64 |
Colors of variables: wff set class |
Syntax hints: = wceq 1312 (class class class)co 5726 1c1 7541 · cmul 7545 4c4 8676 5c5 8677 6c6 8678 7c7 8679 8c8 8680 ;cdc 9079 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 586 ax-in2 587 ax-io 681 ax-5 1404 ax-7 1405 ax-gen 1406 ax-ie1 1450 ax-ie2 1451 ax-8 1463 ax-10 1464 ax-11 1465 ax-i12 1466 ax-bndl 1467 ax-4 1468 ax-14 1473 ax-17 1487 ax-i9 1491 ax-ial 1495 ax-i5r 1496 ax-ext 2095 ax-sep 4004 ax-pow 4056 ax-pr 4089 ax-setind 4410 ax-cnex 7629 ax-resscn 7630 ax-1cn 7631 ax-1re 7632 ax-icn 7633 ax-addcl 7634 ax-addrcl 7635 ax-mulcl 7636 ax-addcom 7638 ax-mulcom 7639 ax-addass 7640 ax-mulass 7641 ax-distr 7642 ax-i2m1 7643 ax-1rid 7645 ax-0id 7646 ax-rnegex 7647 ax-cnre 7649 |
This theorem depends on definitions: df-bi 116 df-3an 945 df-tru 1315 df-fal 1318 df-nf 1418 df-sb 1717 df-eu 1976 df-mo 1977 df-clab 2100 df-cleq 2106 df-clel 2109 df-nfc 2242 df-ne 2281 df-ral 2393 df-rex 2394 df-reu 2395 df-rab 2397 df-v 2657 df-sbc 2877 df-dif 3037 df-un 3039 df-in 3041 df-ss 3048 df-pw 3476 df-sn 3497 df-pr 3498 df-op 3500 df-uni 3701 df-int 3736 df-br 3894 df-opab 3948 df-id 4173 df-xp 4503 df-rel 4504 df-cnv 4505 df-co 4506 df-dm 4507 df-iota 5044 df-fun 5081 df-fv 5087 df-riota 5682 df-ov 5729 df-oprab 5730 df-mpo 5731 df-sub 7851 df-inn 8624 df-2 8682 df-3 8683 df-4 8684 df-5 8685 df-6 8686 df-7 8687 df-8 8688 df-9 8689 df-n0 8875 df-dec 9080 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |