ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  rabid GIF version

Theorem rabid 2670
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 2481 . 2 {𝑥𝐴𝜑} = {𝑥 ∣ (𝑥𝐴𝜑)}
21abeq2i 2304 1 (𝑥 ∈ {𝑥𝐴𝜑} ↔ (𝑥𝐴𝜑))
Colors of variables: wff set class
Syntax hints:  wa 104  wb 105  wcel 2164  {crab 2476
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-ext 2175
This theorem depends on definitions:  df-bi 117  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-rab 2481
This theorem is referenced by:  rabeq2i  2757  rabn0m  3474  repizf2lem  4190  rabxfrd  4498  onintrab2im  4546  tfis  4611  nnwosdc  12163  imasnopn  14438
  Copyright terms: Public domain W3C validator