Theorem rabid 1766

Description: An "identity" law of concretion for restricted abstraction. Special case of Definition 2.1 of [Quine] p. 16.

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 1649	. 2 |- {x e. A | ph} = {x | (x e. A /\ ph)}
2	1	abeq2i 1567	1 |- (x e. {x e. A | ph} <-> (x e. A /\ ph))

Syntax hints:   <-> wb 146   /\ wa 223   e. wcel 956  {crab 1645

This theorem is referenced by:  rabeq2i 1806  rabxfr 2897  reuunixfr 2901  nnwos 6400  resslogrn 8692

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 961  ax-12 966  ax-17 969  ax-4 971  ax-5o 973  ax-6o 976  ax-9o 1121  ax-ext 1457

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 979  df-sb 1170  df-clab 1462  df-cleq 1467  df-clel 1470  df-rab 1649

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