Theorem xnegeqi

Description: Equality of two extended numbers with -e in front of them. (Contributed by Glauco Siliprandi, 2-Jan-2022)

	Ref	Expression
Hypothesis	xnegeqi.1	⊢ 𝐴 = 𝐵
Assertion	xnegeqi	⊢ -𝑒 𝐴 = -𝑒 𝐵

Proof

Step	Hyp	Ref	Expression
1		xnegeqi.1	⊢ 𝐴 = 𝐵
2		xnegeq	⊢ ( 𝐴 = 𝐵 → -𝑒 𝐴 = -𝑒 𝐵 )
3	1 2	ax-mp	⊢ -𝑒 𝐴 = -𝑒 𝐵