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Theorem elabg2 7031
 Description: One implication of elabg 2665. (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 2160 . 2 xA
2 nfv 1402 . 2 xψ
3 elabg2.1 . 2 (x = A → (ψφ))
41, 2, 3elabgf2 7026 1 (A 𝑉 → (ψA {xφ}))
 Colors of variables: wff set class Syntax hints:   → wi 4   = wceq 1228   ∈ wcel 1374  {cab 2008 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 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004 This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-v 2537 This theorem is referenced by: (None)
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