Theorem wlimeq1

Description: Equality theorem for the limit class. (Contributed by Scott Fenton, 15-Jun-2018)

	Ref	Expression
Assertion	wlimeq1	⊢ ( 𝑅 = 𝑆 → WLim ( 𝑅 , 𝐴 ) = WLim ( 𝑆 , 𝐴 ) )

Proof

Step	Hyp	Ref	Expression
1		eqid	⊢ 𝐴 = 𝐴
2		wlimeq12	⊢ ( ( 𝑅 = 𝑆 ∧ 𝐴 = 𝐴 ) → WLim ( 𝑅 , 𝐴 ) = WLim ( 𝑆 , 𝐴 ) )
3	1 2	mpan2	⊢ ( 𝑅 = 𝑆 → WLim ( 𝑅 , 𝐴 ) = WLim ( 𝑆 , 𝐴 ) )