Theorem rabbii 2716

Description: Equivalent wff's correspond to equal restricted class abstractions. Inference form of rabbidv 2719. (Contributed by Peter Mazsa, 1-Nov-2019.)

Hypothesis

Ref	Expression
rabbii.1	⊢ (𝜑 ↔ 𝜓)

Assertion

Ref	Expression
rabbii	⊢ {𝑥 ∈ 𝐴 ∣ 𝜑} = {𝑥 ∈ 𝐴 ∣ 𝜓}

Proof of Theorem rabbii

Step	Hyp	Ref	Expression
1		rabbii.1	. . 3 ⊢ (𝜑 ↔ 𝜓)
2	1	a1i 9	. 2 ⊢ (𝑥 ∈ 𝐴 → (𝜑 ↔ 𝜓))
3	2	rabbiia 2715	1 ⊢ {𝑥 ∈ 𝐴 ∣ 𝜑} = {𝑥 ∈ 𝐴 ∣ 𝜓}

Syntax hints:   ↔ wb 104   = wceq 1348   ∈ wcel 2141  {crab 2452

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-11 1499  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152

This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-rab 2457

This theorem is referenced by:  dfdif3  3237  suplocexpr  7687  dmtopon  12815