Theorem rabswap

Description: Swap with a membership relation in a restricted class abstraction. (Contributed by NM, 4-Jul-2005)

	Ref	Expression
Assertion	rabswap	⊢ { 𝑥 ∈ 𝐴 ∣ 𝑥 ∈ 𝐵 } = { 𝑥 ∈ 𝐵 ∣ 𝑥 ∈ 𝐴 }

Proof

Step	Hyp	Ref	Expression
1		ancom	⊢ ( ( 𝑥 ∈ 𝐴 ∧ 𝑥 ∈ 𝐵 ) ↔ ( 𝑥 ∈ 𝐵 ∧ 𝑥 ∈ 𝐴 ) )
2	1	rabbia2	⊢ { 𝑥 ∈ 𝐴 ∣ 𝑥 ∈ 𝐵 } = { 𝑥 ∈ 𝐵 ∣ 𝑥 ∈ 𝐴 }