Theorem rabid 2787

Description: An "identity" law of concretion for restricted abstraction. Special case of Definition 2.1 of [Quine] p. 16. (Contributed by NM, 9-Oct-2003.)

Assertion

Ref	Expression
rabid	|- (x e. {x e. A | ph} <-> (x e. A /\ ph))

Proof of Theorem rabid

Step	Hyp	Ref	Expression
1		df-rab 2623	. 2 |- {x e. A | ph} = {x | (x e. A /\ ph)}
2	1	abeq2i 2460	1 |- (x e. {x e. A | ph} <-> (x e. A /\ ph))

Syntax hints:   <-> wb 176   /\ wa 358   e. wcel 1710  {crab 2618

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-rab 2623

This theorem is referenced by:  rabeq2i  2856