Metamath Proof Explorer


Theorem negeqi

Description: Equality inference for negatives. (Contributed by NM, 14-Feb-1995)

Ref Expression
Hypothesis negeqi.1 ⊢ 𝐴 = 𝐵
Assertion negeqi - 𝐴 = - 𝐵

Proof

Step Hyp Ref Expression
1 negeqi.1 ⊢ 𝐴 = 𝐵
2 negeq ⊢ ( 𝐴 = 𝐵 → - 𝐴 = - 𝐵 )
3 1 2 ax-mp ⊢ - 𝐴 = - 𝐵