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Metamath Proof Explorer
Description: If a number is zero, then its square is zero. (Contributed by FL, 10-Dec-2006)
|
|
Ref |
Expression |
|
Assertion |
sq0i |
⊢ ( 𝐴 = 0 → ( 𝐴 ↑ 2 ) = 0 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
oveq1 |
⊢ ( 𝐴 = 0 → ( 𝐴 ↑ 2 ) = ( 0 ↑ 2 ) ) |
| 2 |
|
sq0 |
⊢ ( 0 ↑ 2 ) = 0 |
| 3 |
1 2
|
eqtrdi |
⊢ ( 𝐴 = 0 → ( 𝐴 ↑ 2 ) = 0 ) |