Description: 3 to the power of 7 equals 2187. (Contributed by metakunt, 21-Aug-2024)
Ref | Expression | ||
---|---|---|---|
Assertion | 3exp7 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3nn0 | ||
2 | 6nn0 | ||
3 | 6p1e7 | ||
4 | 7nn0 | ||
5 | 2nn0 | ||
6 | 4 5 | deccl | |
7 | 9nn0 | ||
8 | 3cn | ||
9 | 2cn | ||
10 | 3t2e6 | ||
11 | 8 9 10 | mulcomli | |
12 | 3exp3 | ||
13 | 5 4 | deccl | |
14 | eqid | ||
15 | 1nn0 | ||
16 | 8nn0 | ||
17 | 15 16 | deccl | |
18 | 0nn0 | ||
19 | 5 | dec0h | |
20 | eqid | ||
21 | 13 | nn0cni | |
22 | 21 | mul02i | |
23 | 6cn | ||
24 | ax-1cn | ||
25 | 23 24 3 | addcomli | |
26 | 22 25 | oveq12i | |
27 | 7cn | ||
28 | 27 | addid2i | |
29 | 26 28 | eqtri | |
30 | 16 | dec0h | |
31 | 2t2e4 | ||
32 | 9 | addid2i | |
33 | 31 32 | oveq12i | |
34 | 4p2e6 | ||
35 | 33 34 | eqtri | |
36 | 4nn0 | ||
37 | 7t2e14 | ||
38 | 27 9 37 | mulcomli | |
39 | 1p1e2 | ||
40 | 8cn | ||
41 | 4cn | ||
42 | 8p4e12 | ||
43 | 40 41 42 | addcomli | |
44 | 15 36 16 38 39 5 43 | decaddci | |
45 | 5 4 18 16 14 30 5 5 5 35 44 | decma2c | |
46 | 18 5 15 16 19 20 13 5 2 29 45 | decmac | |
47 | 4p4e8 | ||
48 | 15 36 36 37 47 | decaddi | |
49 | 7t7e49 | ||
50 | 4 5 4 14 7 36 48 49 | decmul2c | |
51 | 13 5 4 14 7 17 46 50 | decmul1c | |
52 | 1 1 11 12 51 | numexp2x | |
53 | eqid | ||
54 | 7t3e21 | ||
55 | 1p0e1 | ||
56 | 5 15 18 54 55 | decaddi | |
57 | 11 | oveq1i | |
58 | 6p2e8 | ||
59 | 57 58 | eqtri | |
60 | 4 5 18 5 53 19 1 56 59 | decma | |
61 | 9t3e27 | ||
62 | 1 6 7 52 4 5 60 61 | decmul1c | |
63 | 1 2 3 62 | numexpp1 |