Theorem rabeqdv

Description: Equality of restricted class abstractions. Deduction form of rabeq . (Contributed by Glauco Siliprandi, 5-Apr-2020)

	Ref	Expression
Hypothesis	rabeqdv.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	rabeqdv	⊢ ( 𝜑 → { 𝑥 ∈ 𝐴 ∣ 𝜓 } = { 𝑥 ∈ 𝐵 ∣ 𝜓 } )

Proof

Step	Hyp	Ref	Expression
1		rabeqdv.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		rabeq	⊢ ( 𝐴 = 𝐵 → { 𝑥 ∈ 𝐴 ∣ 𝜓 } = { 𝑥 ∈ 𝐵 ∣ 𝜓 } )
3	1 2	syl	⊢ ( 𝜑 → { 𝑥 ∈ 𝐴 ∣ 𝜓 } = { 𝑥 ∈ 𝐵 ∣ 𝜓 } )