Theorem wlimss

Description: The class of limit points is a subclass of the base class. (Contributed by Scott Fenton, 16-Jun-2018)

	Ref	Expression
Assertion	wlimss	⊢ WLim ( 𝑅 , 𝐴 ) ⊆ 𝐴

Proof

Step	Hyp	Ref	Expression
1		df-wlim	⊢ WLim ( 𝑅 , 𝐴 ) = { 𝑥 ∈ 𝐴 ∣ ( 𝑥 ≠ inf ( 𝐴 , 𝐴 , 𝑅 ) ∧ 𝑥 = sup ( Pred ( 𝑅 , 𝐴 , 𝑥 ) , 𝐴 , 𝑅 ) ) }
2	1	ssrab3	⊢ WLim ( 𝑅 , 𝐴 ) ⊆ 𝐴