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Metamath Proof Explorer
Theorem sq0
Description: The square of 0 is 0. (Contributed by NM, 6-Jun-2006)
|
|
Ref |
Expression |
|
Assertion |
sq0 |
⊢ ( 0 ↑ 2 ) = 0 |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
eqid |
⊢ 0 = 0 |
| 2 |
|
0cn |
⊢ 0 ∈ ℂ |
| 3 |
2
|
sqeq0i |
⊢ ( ( 0 ↑ 2 ) = 0 ↔ 0 = 0 ) |
| 4 |
1 3
|
mpbir |
⊢ ( 0 ↑ 2 ) = 0 |