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Mirrors > Home > ILE Home > Th. List > 6t4e24 | GIF version |
Description: 6 times 4 equals 24. (Contributed by Mario Carneiro, 19-Apr-2015.) |
Ref | Expression |
---|---|
6t4e24 | ⊢ (6 · 4) = ;24 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 6nn0 8850 | . 2 ⊢ 6 ∈ ℕ0 | |
2 | 3nn0 8847 | . 2 ⊢ 3 ∈ ℕ0 | |
3 | df-4 8639 | . 2 ⊢ 4 = (3 + 1) | |
4 | 6t3e18 9138 | . 2 ⊢ (6 · 3) = ;18 | |
5 | 1nn0 8845 | . . 3 ⊢ 1 ∈ ℕ0 | |
6 | 8nn0 8852 | . . 3 ⊢ 8 ∈ ℕ0 | |
7 | eqid 2100 | . . 3 ⊢ ;18 = ;18 | |
8 | 1p1e2 8695 | . . 3 ⊢ (1 + 1) = 2 | |
9 | 4nn0 8848 | . . 3 ⊢ 4 ∈ ℕ0 | |
10 | 8p6e14 9117 | . . 3 ⊢ (8 + 6) = ;14 | |
11 | 5, 6, 1, 7, 8, 9, 10 | decaddci 9094 | . 2 ⊢ (;18 + 6) = ;24 |
12 | 1, 2, 3, 4, 11 | 4t3lem 9130 | 1 ⊢ (6 · 4) = ;24 |
Colors of variables: wff set class |
Syntax hints: = wceq 1299 (class class class)co 5706 1c1 7501 · cmul 7505 2c2 8629 3c3 8630 4c4 8631 6c6 8633 8c8 8635 ;cdc 9034 |
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 584 ax-in2 585 ax-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-14 1460 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 ax-sep 3986 ax-pow 4038 ax-pr 4069 ax-setind 4390 ax-cnex 7586 ax-resscn 7587 ax-1cn 7588 ax-1re 7589 ax-icn 7590 ax-addcl 7591 ax-addrcl 7592 ax-mulcl 7593 ax-addcom 7595 ax-mulcom 7596 ax-addass 7597 ax-mulass 7598 ax-distr 7599 ax-i2m1 7600 ax-1rid 7602 ax-0id 7603 ax-rnegex 7604 ax-cnre 7606 |
This theorem depends on definitions: df-bi 116 df-3an 932 df-tru 1302 df-fal 1305 df-nf 1405 df-sb 1704 df-eu 1963 df-mo 1964 df-clab 2087 df-cleq 2093 df-clel 2096 df-nfc 2229 df-ne 2268 df-ral 2380 df-rex 2381 df-reu 2382 df-rab 2384 df-v 2643 df-sbc 2863 df-dif 3023 df-un 3025 df-in 3027 df-ss 3034 df-pw 3459 df-sn 3480 df-pr 3481 df-op 3483 df-uni 3684 df-int 3719 df-br 3876 df-opab 3930 df-id 4153 df-xp 4483 df-rel 4484 df-cnv 4485 df-co 4486 df-dm 4487 df-iota 5024 df-fun 5061 df-fv 5067 df-riota 5662 df-ov 5709 df-oprab 5710 df-mpo 5711 df-sub 7806 df-inn 8579 df-2 8637 df-3 8638 df-4 8639 df-5 8640 df-6 8641 df-7 8642 df-8 8643 df-9 8644 df-n0 8830 df-dec 9035 |
This theorem is referenced by: 6t5e30 9140 fac4 10320 |
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