Metamath Proof Explorer


Theorem negeq

Description: Equality theorem for negatives. (Contributed by NM, 10-Feb-1995)

Ref Expression
Assertion negeq ⊢ A = B → − A = − B

Proof

Step Hyp Ref Expression
1 oveq2 ⊢ A = B → 0 − A = 0 − B
2 df-neg ⊢ − A = 0 − A
3 df-neg ⊢ − B = 0 − B
4 1 2 3 3eqtr4g ⊢ A = B → − A = − B