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Theorem rabid 2542
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 2368 . 2 {𝑥𝐴𝜑} = {𝑥 ∣ (𝑥𝐴𝜑)}
21abeq2i 2198 1 (𝑥 ∈ {𝑥𝐴𝜑} ↔ (𝑥𝐴𝜑))
Colors of variables: wff set class
Syntax hints:  wa 102  wb 103  wcel 1438  {crab 2363
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-rab 2368
This theorem is referenced by:  rabeq2i  2616  rabn0m  3308  repizf2lem  3988  rabxfrd  4282  onintrab2im  4325  tfis  4388
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