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 )