Theorem rabbii 2598

Description: Equivalent wff's correspond to equal restricted class abstractions. Inference form of rabbidv 2601. (Contributed by Peter Mazsa, 1-Nov-2019.)

Hypothesis

Ref	Expression
rabbii.1	|- ( ph <-> ps )

Assertion

Ref	Expression
rabbii	|- { x e. A | ph } = { x e. A | ps }

Proof of Theorem rabbii

Step	Hyp	Ref	Expression
1		rabbii.1	. . 3 |- ( ph <-> ps )
2	1	a1i 9	. 2 |- ( x e. A -> ( ph <-> ps ) )
3	2	rabbiia 2597	1 |- { x e. A | ph } = { x e. A | ps }

Syntax hints:   <-> wb 103   = wceq 1285   e. wcel 1434   {crab 2357

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065

This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-rab 2362

This theorem is referenced by:  dfdif3  3094