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Theorem cbvixp 6849
 Description: Change bound variable in an indexed Cartesian product. (Contributed by Jeff Madsen, 20-Jun-2011.)
Hypotheses
Ref Expression
cbvixp.1
cbvixp.2
cbvixp.3
Assertion
Ref Expression
cbvixp
Distinct variable group:   ,,
Allowed substitution hints:   (,)   (,)

Proof of Theorem cbvixp
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 cbvixp.1 . . . . . 6
21nfel2 2444 . . . . 5
3 cbvixp.2 . . . . . 6
43nfel2 2444 . . . . 5
5 fveq2 5541 . . . . . 6
6 cbvixp.3 . . . . . 6
75, 6eleq12d 2364 . . . . 5
82, 4, 7cbvral 2773 . . . 4
98anbi2i 675 . . 3
109abbii 2408 . 2
11 dfixp 6835 . 2
12 dfixp 6835 . 2
1310, 11, 123eqtr4i 2326 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 358   wceq 1632   wcel 1696  cab 2282  wnfc 2419  wral 2556   wfn 5266  cfv 5271  cixp 6833 This theorem is referenced by:  cbvixpv  6850  mptelixpg  6869  ixpiunwdom  7321  prdsbas3  13396  invfuc  13864  elptr2  17285  ptunimpt  17306  ptcldmpt  17324 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-br 4040  df-iota 5235  df-fn 5274  df-fv 5279  df-ixp 6834
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