NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  cbviunv Unicode version

Theorem cbviunv 4005
Description: Rule used to change the bound variables in an indexed union, with the substitution specified implicitly by the hypothesis. (Contributed by NM, 15-Sep-2003.)
Hypothesis
Ref Expression
cbviunv.1
Assertion
Ref Expression
cbviunv
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem cbviunv
StepHypRef Expression
1 nfcv 2489 . 2  F/_
2 nfcv 2489 . 2  F/_
3 cbviunv.1 . 2
41, 2, 3cbviun 4003 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wceq 1642  ciun 3969
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-rex 2620  df-iun 3971
This theorem is referenced by:  iunxdif2  4014
  Copyright terms: Public domain W3C validator