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Theorem inex1g 3867
Description: Closed-form, generalized Separation Scheme. (Contributed by NM, 7-Apr-1995.)
Assertion
Ref Expression
inex1g (A 𝑉 → (AB) V)

Proof of Theorem inex1g
Dummy variable x is distinct from all other variables.
StepHypRef Expression
1 ineq1 3108 . . 3 (x = A → (xB) = (AB))
21eleq1d 2088 . 2 (x = A → ((xB) V ↔ (AB) V))
3 vex 2538 . . 3 x V
43inex1 3865 . 2 (xB) V
52, 4vtoclg 2590 1 (A 𝑉 → (AB) V)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1228   wcel 1374  Vcvv 2535  cin 2893
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  ax-sep 3849
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  df-in 2901
This theorem is referenced by:  onin  4072  dmresexg  4561  funimaexg  4909  offval  5642  offval3  5684
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