Theorem negeqd

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

	Ref	Expression
Hypothesis	negeqd.1	$$⊢\phi \to A=B$$
Assertion	negeqd	$$⊢\phi \to -A=-B$$

Proof

Step	Hyp	Ref	Expression
1		negeqd.1	$$⊢\phi \to A=B$$
2		negeq	$$⊢A=B\to -A=-B$$
3	1 2	syl	$$⊢\phi \to -A=-B$$