Theorem rabbii 2749

Description: Equivalent wff's correspond to equal restricted class abstractions. Inference form of rabbidv 2752. (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 2748	1 |- { x e. A | ph } = { x e. A | ps }

Syntax hints:   <-> wb 105   = wceq 1364   e. wcel 2167   {crab 2479

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-11 1520  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-rab 2484

This theorem is referenced by:  dfdif3  3273  suplocexpr  7792  dfrhm2  13710  dmtopon  14259