Theorem xnegeqd

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

	Ref	Expression
Hypothesis	xnegeqd.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	xnegeqd	⊢ ( 𝜑 → -𝑒 𝐴 = -𝑒 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		xnegeqd.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		xnegeq	⊢ ( 𝐴 = 𝐵 → -𝑒 𝐴 = -𝑒 𝐵 )
3	1 2	syl	⊢ ( 𝜑 → -𝑒 𝐴 = -𝑒 𝐵 )