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Theorem elab2a 14974
Description: One implication of elab 2896. (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 1539 . 2 𝑥𝜓
2 elab2a.s . 2 𝐴 ∈ V
3 elab2a.1 . 2 (𝑥 = 𝐴 → (𝜓𝜑))
41, 2, 3elabf2 14972 1 (𝜓𝐴 ∈ {𝑥𝜑})
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1364  wcel 2160  {cab 2175  Vcvv 2752
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-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754
This theorem is referenced by: (None)
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