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Theorem cbvdisj 4432
Description: Change bound variables in a disjoint collection. (Contributed by Mario Carneiro, 14-Nov-2016.)
Hypotheses
Ref Expression
cbvdisj.1
cbvdisj.2
cbvdisj.3
Assertion
Ref Expression
cbvdisj
Distinct variable group:   , ,

Proof of Theorem cbvdisj
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 cbvdisj.1 . . . . 5
21nfcri 2612 . . . 4
3 cbvdisj.2 . . . . 5
43nfcri 2612 . . . 4
5 cbvdisj.3 . . . . 5
65eleq2d 2527 . . . 4
72, 4, 6cbvrmo 3083 . . 3
87albii 1640 . 2
9 df-disj 4423 . 2
10 df-disj 4423 . 2
118, 9, 103bitr4i 277 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  A.wal 1393  =wceq 1395  e.wcel 1818  F/_wnfc 2605  E*wrmo 2810  Disj_wdisj 4422
This theorem is referenced by:  cbvdisjv  4433  disjors  4438  disjxiun  4449  volfiniun  21957  voliun  21964
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-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-reu 2814  df-rmo 2815  df-disj 4423
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