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Theorem inex1g 3856
 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 3099 . . 3 (x = A → (xB) = (AB))
21eleq1d 2079 . 2 (x = A → ((xB) V ↔ (AB) V))
3 vex 2529 . . 3 x V
43inex1 3854 . 2 (xB) V
52, 4vtoclg 2581 1 (A 𝑉 → (AB) V)
 Colors of variables: wff set class Syntax hints:   → wi 4   = wceq 1223   ∈ wcel 1366  Vcvv 2526   ∩ cin 2884 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 614  ax-5 1309  ax-7 1310  ax-gen 1311  ax-ie1 1355  ax-ie2 1356  ax-8 1368  ax-10 1369  ax-11 1370  ax-i12 1371  ax-bnd 1372  ax-4 1373  ax-17 1392  ax-i9 1396  ax-ial 1400  ax-i5r 1401  ax-ext 1995  ax-sep 3838 This theorem depends on definitions:  df-bi 110  df-tru 1226  df-nf 1323  df-sb 1619  df-clab 2000  df-cleq 2006  df-clel 2009  df-nfc 2140  df-v 2528  df-in 2892 This theorem is referenced by:  onin  4061  dmresexg  4549  funimaexg  4897  offval  5630  offval3  5672
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