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Metamath Proof Explorer

Theorem negeqd

Description: Equality deduction for negatives. (Contributed by NM, 14-May-1999)

Ref Expression
Hypothesis negeqd.1 ⊢ φ → A = B
Assertion negeqd ⊢ φ → − A = − B

Proof

Step Hyp Ref Expression
1 negeqd.1 ⊢ φ → A = B
2 negeq ⊢ A = B → − A = − B
3 1 2 syl ⊢ φ → − A = − B