Theorem rabbii 2707

Description: Equivalent wff's correspond to equal restricted class abstractions. Inference form of rabbidv 2710. (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 2706	1 |- { x e. A | ph } = { x e. A | ps }

Syntax hints:   <-> wb 104   = wceq 1342   e. wcel 2135   {crab 2446

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 1434  ax-7 1435  ax-gen 1436  ax-ie1 1480  ax-ie2 1481  ax-8 1491  ax-11 1493  ax-4 1497  ax-17 1513  ax-i9 1517  ax-ial 1521  ax-i5r 1522  ax-ext 2146

This theorem depends on definitions:  df-bi 116  df-tru 1345  df-nf 1448  df-sb 1750  df-clab 2151  df-cleq 2157  df-rab 2451

This theorem is referenced by:  dfdif3  3227  suplocexpr  7657  dmtopon  12562