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Theorem elabf2 9190
Description: One implication of elabf 2680. (Contributed by BJ, 21-Nov-2019.)
Hypotheses
Ref Expression
elabf2.nf xψ
elabf2.s A V
elabf2.1 (x = A → (ψφ))
Assertion
Ref Expression
elabf2 (ψA {xφ})
Distinct variable group:   x,A
Allowed substitution hints:   φ(x)   ψ(x)

Proof of Theorem elabf2
StepHypRef Expression
1 elabf2.s . 2 A V
2 nfcv 2175 . . 3 xA
3 elabf2.nf . . 3 xψ
4 elabf2.1 . . 3 (x = A → (ψφ))
52, 3, 4elabgf2 9188 . 2 (A V → (ψA {xφ}))
61, 5ax-mp 7 1 (ψA {xφ})
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1242  wnf 1346   wcel 1390  {cab 2023  Vcvv 2551
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553
This theorem is referenced by:  elab2a  9192  bj-bdfindis  9335
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