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Theorem dfixp 6601
 Description: Eliminate the expression in df-ixp 6600, under the assumption that and are disjoint. This way, we can say that is bound in even if it appears free in . (Contributed by Mario Carneiro, 12-Aug-2016.)
Assertion
Ref Expression
dfixp
Distinct variable groups:   ,,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem dfixp
StepHypRef Expression
1 df-ixp 6600 . 2
2 abid2 2261 . . . . 5
32fneq2i 5225 . . . 4
43anbi1i 454 . . 3
54abbii 2256 . 2
61, 5eqtri 2161 1
 Colors of variables: wff set class Syntax hints:   wa 103   wceq 1332   wcel 1481  cab 2126  wral 2417   wfn 5125  cfv 5130  cixp 6599 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-11 1485  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-fn 5133  df-ixp 6600 This theorem is referenced by:  ixpsnval  6602  elixp2  6603  ixpeq1  6610  cbvixp  6616  ixp0x  6627
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