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Theorem cbvdisj 4192
 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 Disj Disj
Distinct variable group:   ,,
Allowed substitution hints:   (,)   (,)

Proof of Theorem cbvdisj
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 cbvdisj.1 . . . . 5
21nfcri 2566 . . . 4
3 cbvdisj.2 . . . . 5
43nfcri 2566 . . . 4
5 cbvdisj.3 . . . . 5
65eleq2d 2503 . . . 4
72, 4, 6cbvrmo 2931 . . 3
87albii 1575 . 2
9 df-disj 4183 . 2 Disj
10 df-disj 4183 . 2 Disj
118, 9, 103bitr4i 269 1 Disj Disj
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wal 1549   wceq 1652   wcel 1725  wnfc 2559  wrmo 2708  Disj wdisj 4182 This theorem is referenced by:  cbvdisjv  4193  disjors  4198  disjxiun  4209  volfiniun  19441  voliun  19448 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-reu 2712  df-rmo 2713  df-disj 4183
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