Mathbox for Thierry Arnoux < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  cbviunf Structured version   Visualization version   Unicode version

Theorem cbviunf 28247
 Description: Rule used to change the bound variables in an indexed union, with the substitution specified implicitly by the hypothesis. (Contributed by NM, 26-Mar-2006.) (Revised by Andrew Salmon, 25-Jul-2011.)
Hypotheses
Ref Expression
cbviunf.x
cbviunf.y
cbviunf.1
cbviunf.2
cbviunf.3
Assertion
Ref Expression
cbviunf
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)   (,)

Proof of Theorem cbviunf
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 cbviunf.x . . . 4
2 cbviunf.y . . . 4
3 cbviunf.1 . . . . 5
43nfcri 2606 . . . 4
5 cbviunf.2 . . . . 5
65nfcri 2606 . . . 4
7 cbviunf.3 . . . . 5
87eleq2d 2534 . . . 4
91, 2, 4, 6, 8cbvrexf 3000 . . 3
109abbii 2587 . 2
11 df-iun 4271 . 2
12 df-iun 4271 . 2
1310, 11, 123eqtr4i 2503 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1452   wcel 1904  cab 2457  wnfc 2599  wrex 2757  ciun 4269 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ral 2761  df-rex 2762  df-iun 4271 This theorem is referenced by:  aciunf1lem  28339
 Copyright terms: Public domain W3C validator