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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 9200 | . 2 ⊢ 6 ∈ ℕ0 | |
2 | 3nn0 9197 | . 2 ⊢ 3 ∈ ℕ0 | |
3 | df-4 8983 | . 2 ⊢ 4 = (3 + 1) | |
4 | 6t3e18 9491 | . 2 ⊢ (6 · 3) = ;18 | |
5 | 1nn0 9195 | . . 3 ⊢ 1 ∈ ℕ0 | |
6 | 8nn0 9202 | . . 3 ⊢ 8 ∈ ℕ0 | |
7 | eqid 2177 | . . 3 ⊢ ;18 = ;18 | |
8 | 1p1e2 9039 | . . 3 ⊢ (1 + 1) = 2 | |
9 | 4nn0 9198 | . . 3 ⊢ 4 ∈ ℕ0 | |
10 | 8p6e14 9470 | . . 3 ⊢ (8 + 6) = ;14 | |
11 | 5, 6, 1, 7, 8, 9, 10 | decaddci 9447 | . 2 ⊢ (;18 + 6) = ;24 |
12 | 1, 2, 3, 4, 11 | 4t3lem 9483 | 1 ⊢ (6 · 4) = ;24 |
Colors of variables: wff set class |
Syntax hints: = wceq 1353 (class class class)co 5878 1c1 7815 · cmul 7819 2c2 8973 3c3 8974 4c4 8975 6c6 8977 8c8 8979 ;cdc 9387 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-sep 4123 ax-pow 4176 ax-pr 4211 ax-setind 4538 ax-cnex 7905 ax-resscn 7906 ax-1cn 7907 ax-1re 7908 ax-icn 7909 ax-addcl 7910 ax-addrcl 7911 ax-mulcl 7912 ax-addcom 7914 ax-mulcom 7915 ax-addass 7916 ax-mulass 7917 ax-distr 7918 ax-i2m1 7919 ax-1rid 7921 ax-0id 7922 ax-rnegex 7923 ax-cnre 7925 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-ral 2460 df-rex 2461 df-reu 2462 df-rab 2464 df-v 2741 df-sbc 2965 df-dif 3133 df-un 3135 df-in 3137 df-ss 3144 df-pw 3579 df-sn 3600 df-pr 3601 df-op 3603 df-uni 3812 df-int 3847 df-br 4006 df-opab 4067 df-id 4295 df-xp 4634 df-rel 4635 df-cnv 4636 df-co 4637 df-dm 4638 df-iota 5180 df-fun 5220 df-fv 5226 df-riota 5834 df-ov 5881 df-oprab 5882 df-mpo 5883 df-sub 8133 df-inn 8923 df-2 8981 df-3 8982 df-4 8983 df-5 8984 df-6 8985 df-7 8986 df-8 8987 df-9 8988 df-n0 9180 df-dec 9388 |
This theorem is referenced by: 6t5e30 9493 fac4 10716 |
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