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Theorem elabg2 9193
Description: One implication of elabg 2682. (Contributed by BJ, 21-Nov-2019.)
Hypothesis
Ref Expression
elabg2.1 (x = A → (ψφ))
Assertion
Ref Expression
elabg2 (A 𝑉 → (ψA {xφ}))
Distinct variable groups:   ψ,x   x,A
Allowed substitution hints:   φ(x)   𝑉(x)

Proof of Theorem elabg2
StepHypRef Expression
1 nfcv 2175 . 2 xA
2 nfv 1418 . 2 xψ
3 elabg2.1 . 2 (x = A → (ψφ))
41, 2, 3elabgf2 9188 1 (A 𝑉 → (ψA {xφ}))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1242   wcel 1390  {cab 2023
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: (None)
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