Theorem rp-abid

Description: Two ways to express a class. (Contributed by RP, 13-Feb-2025)

	Ref	Expression
Assertion	rp-abid	⊢ 𝐴 = { 𝑥 ∣ ∃ 𝑎 ∈ 𝐴 𝑥 = 𝑎 }

Proof

Step	Hyp	Ref	Expression
1		clel5	⊢ ( 𝑥 ∈ 𝐴 ↔ ∃ 𝑎 ∈ 𝐴 𝑥 = 𝑎 )
2	1	eqabi	⊢ 𝐴 = { 𝑥 ∣ ∃ 𝑎 ∈ 𝐴 𝑥 = 𝑎 }