Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  dfixp Structured version   Unicode version

Theorem dfixp 7532
 Description: Eliminate the expression in df-ixp 7531, 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 7531 . 2
2 abid2 2569 . . . . 5
32fneq2i 5689 . . . 4
43anbi1i 699 . . 3
54abbii 2563 . 2
61, 5eqtri 2458 1
 Colors of variables: wff setvar class Syntax hints:   wa 370   wceq 1437   wcel 1870  cab 2414  wral 2782   wfn 5596  cfv 5601  cixp 7530 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407 This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-fn 5604  df-ixp 7531 This theorem is referenced by:  ixpsnval  7533  elixp2  7534  ixpeq1  7541  cbvixp  7547  ixp0x  7558
 Copyright terms: Public domain W3C validator