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Theorem rabid 2629
 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 2441 . 2 {𝑥𝐴𝜑} = {𝑥 ∣ (𝑥𝐴𝜑)}
21abeq2i 2265 1 (𝑥 ∈ {𝑥𝐴𝜑} ↔ (𝑥𝐴𝜑))
 Colors of variables: wff set class Syntax hints:   ∧ wa 103   ↔ wb 104   ∈ wcel 2125  {crab 2436 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 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-rab 2441 This theorem is referenced by:  rabeq2i  2706  rabn0m  3417  repizf2lem  4117  rabxfrd  4423  onintrab2im  4471  tfis  4536  imasnopn  12646
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