Metamath Proof Explorer


Theorem sq0id

Description: If a number is zero, its square is zero. Deduction form of sq0i . Converse of sqeq0d . (Contributed by David Moews, 28-Feb-2017)

Ref Expression
Hypothesis sq0id.1
|- ( ph -> A = 0 )
Assertion sq0id
|- ( ph -> ( A ^ 2 ) = 0 )

Proof

Step Hyp Ref Expression
1 sq0id.1
 |-  ( ph -> A = 0 )
2 sq0i
 |-  ( A = 0 -> ( A ^ 2 ) = 0 )
3 1 2 syl
 |-  ( ph -> ( A ^ 2 ) = 0 )