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Theorem rabid 2485
 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 ∈ {𝑥𝐴𝜑} ↔ (𝑥𝐴𝜑))

Proof of Theorem rabid
StepHypRef Expression
1 df-rab 2315 . 2 {𝑥𝐴𝜑} = {𝑥 ∣ (𝑥𝐴𝜑)}
21abeq2i 2148 1 (𝑥 ∈ {𝑥𝐴𝜑} ↔ (𝑥𝐴𝜑))
 Colors of variables: wff set class Syntax hints:   ∧ wa 97   ↔ wb 98   ∈ wcel 1393  {crab 2310 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 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-rab 2315 This theorem is referenced by:  rabeq2i  2554  rabn0m  3245  repizf2lem  3914  rabxfrd  4201  onintrab2im  4244  tfis  4306
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