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Theorem abid2 2314
Description: A simplification of class abstraction. Theorem 5.2 of [Quine] p. 35. (Contributed by NM, 26-Dec-1993.)
Assertion
Ref Expression
abid2 {𝑥𝑥𝐴} = 𝐴
Distinct variable group:   𝑥,𝐴

Proof of Theorem abid2
StepHypRef Expression
1 biid 171 . . 3 (𝑥𝐴𝑥𝐴)
21abbi2i 2308 . 2 𝐴 = {𝑥𝑥𝐴}
32eqcomi 2197 1 {𝑥𝑥𝐴} = 𝐴
Colors of variables: wff set class
Syntax hints:   = wceq 1364  wcel 2164  {cab 2179
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-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-11 1517  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175
This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189
This theorem is referenced by:  csbid  3088  abss  3248  ssab  3249  abssi  3254  notab  3429  inrab2  3432  dfrab2  3434  dfrab3  3435  notrab  3436  eusn  3692  dfopg  3802  iunid  3968  csbexga  4157  imai  5021  dffv4g  5551  frec0g  6450  dfixp  6754  euen1b  6857  acfun  7267  ccfunen  7324
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