Metamath Proof Explorer


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 ) )