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Theorem dfixp 7057
 Description: Eliminate the expression in df-ixp 7056, 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 7056 . 2
2 abid2 2552 . . . . 5
32fneq2i 5532 . . . 4
43anbi1i 677 . . 3
54abbii 2547 . 2
61, 5eqtri 2455 1
 Colors of variables: wff set class Syntax hints:   wa 359   wceq 1652   wcel 1725  cab 2421  wral 2697   wfn 5441  cfv 5446  cixp 7055 This theorem is referenced by:  elixp2  7058  ixpeq1  7065  cbvixp  7071  ixp0x  7082 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-fn 5449  df-ixp 7056
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