Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > mgpbas | Structured version Visualization version GIF version |
Description: Base set of the multiplication group. (Contributed by Mario Carneiro, 21-Dec-2014.) (Revised by Mario Carneiro, 5-Oct-2015.) |
Ref | Expression |
---|---|
mgpbas.1 | ⊢ 𝑀 = (mulGrp‘𝑅) |
mgpbas.2 | ⊢ 𝐵 = (Base‘𝑅) |
Ref | Expression |
---|---|
mgpbas | ⊢ 𝐵 = (Base‘𝑀) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mgpbas.2 | . 2 ⊢ 𝐵 = (Base‘𝑅) | |
2 | mgpbas.1 | . . 3 ⊢ 𝑀 = (mulGrp‘𝑅) | |
3 | df-base 16761 | . . 3 ⊢ Base = Slot 1 | |
4 | 1nn 11841 | . . 3 ⊢ 1 ∈ ℕ | |
5 | 1ne2 12038 | . . 3 ⊢ 1 ≠ 2 | |
6 | 2, 3, 4, 5 | mgplem 19509 | . 2 ⊢ (Base‘𝑅) = (Base‘𝑀) |
7 | 1, 6 | eqtri 2765 | 1 ⊢ 𝐵 = (Base‘𝑀) |
Copyright terms: Public domain | W3C validator |