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Theorem cbvixp 7506
 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:   ,,

Proof of Theorem cbvixp
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 cbvixp.1 . . . . . 6
21nfel2 2637 . . . . 5
3 cbvixp.2 . . . . . 6
43nfel2 2637 . . . . 5
5 fveq2 5871 . . . . . 6
6 cbvixp.3 . . . . . 6
75, 6eleq12d 2539 . . . . 5
82, 4, 7cbvral 3080 . . . 4
98anbi2i 694 . . 3
109abbii 2591 . 2
11 dfixp 7491 . 2
12 dfixp 7491 . 2
1310, 11, 123eqtr4i 2496 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  e.wcel 1818  {cab 2442  F/_wnfc 2605  A.wral 2807  Fnwfn 5588  cfv 5593  X_`cixp 7489 This theorem is referenced by:  cbvixpv  7507  mptelixpg  7526  ixpiunwdom  8038  prdsbas3  14878  elptr2  20075  ptunimpt  20096  ptcldmpt  20115  finixpnum  30038  ptrest  30048 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-iota 5556  df-fn 5596  df-fv 5601  df-ixp 7490
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