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 )