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Theorem elab2a 11026
 Description: One implication of elab 2748. (Contributed by BJ, 21-Nov-2019.)
Hypotheses
Ref Expression
elab2a.s 𝐴 ∈ V
elab2a.1 (𝑥 = 𝐴 → (𝜓𝜑))
Assertion
Ref Expression
elab2a (𝜓𝐴 ∈ {𝑥𝜑})
Distinct variable groups:   𝜓,𝑥   𝑥,𝐴
Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem elab2a
StepHypRef Expression
1 nfv 1462 . 2 𝑥𝜓
2 elab2a.s . 2 𝐴 ∈ V
3 elab2a.1 . 2 (𝑥 = 𝐴 → (𝜓𝜑))
41, 2, 3elabf2 11024 1 (𝜓𝐴 ∈ {𝑥𝜑})
 Colors of variables: wff set class Syntax hints:   → wi 4   = wceq 1285   ∈ wcel 1434  {cab 2069  Vcvv 2612 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-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2614 This theorem is referenced by: (None)
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