Theorem wlimeq2

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

	Ref	Expression
Assertion	wlimeq2	⊢ ( 𝐴 = 𝐵 → WLim ( 𝑅 , 𝐴 ) = WLim ( 𝑅 , 𝐵 ) )

Proof

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