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