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Theorem rabid 2479
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 {x Aφ} ↔ (x A φ))

Proof of Theorem rabid
StepHypRef Expression
1 df-rab 2309 . 2 {x Aφ} = {x ∣ (x A φ)}
21abeq2i 2145 1 (x {x Aφ} ↔ (x A φ))
Colors of variables: wff set class
Syntax hints:   wa 97  wb 98   wcel 1390  {crab 2304
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-rab 2309
This theorem is referenced by:  rabeq2i  2548  rabn0m  3239  repizf2lem  3905  rabxfrd  4167  tfis  4249
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