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Theorem cbvdisjf 23365
 Description: Change bound variables in a disjoint collection. (Contributed by Thierry Arnoux, 6-Apr-2017.)
Hypotheses
Ref Expression
cbvdisjf.1
cbvdisjf.2
cbvdisjf.3
cbvdisjf.4
Assertion
Ref Expression
cbvdisjf Disj Disj
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   (,)   (,)

Proof of Theorem cbvdisjf
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfv 1609 . . . . . 6
2 cbvdisjf.2 . . . . . . 7
32nfcri 2426 . . . . . 6
41, 3nfan 1783 . . . . 5
5 nfcv 2432 . . . . . . 7
6 cbvdisjf.1 . . . . . . 7
75, 6nfel 2440 . . . . . 6
8 cbvdisjf.3 . . . . . . 7
98nfcri 2426 . . . . . 6
107, 9nfan 1783 . . . . 5
11 eleq1 2356 . . . . . 6
12 cbvdisjf.4 . . . . . . 7
1312eleq2d 2363 . . . . . 6
1411, 13anbi12d 691 . . . . 5
154, 10, 14cbvmo 2193 . . . 4
16 df-rmo 2564 . . . 4
17 df-rmo 2564 . . . 4
1815, 16, 173bitr4i 268 . . 3
1918albii 1556 . 2
20 df-disj 4010 . 2 Disj
21 df-disj 4010 . 2 Disj
2219, 20, 213bitr4i 268 1 Disj Disj
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358  wal 1530   wceq 1632   wcel 1696  wmo 2157  wnfc 2419  wrmo 2559  Disj wdisj 4009 This theorem is referenced by:  disjorsf  23372 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rmo 2564  df-disj 4010
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