Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  cbvdisj Structured version   Unicode version

Theorem cbvdisj 4433
 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 2622 . . . 4
3 cbvdisj.2 . . . . 5
43nfcri 2622 . . . 4
5 cbvdisj.3 . . . . 5
65eleq2d 2537 . . . 4
72, 4, 6cbvrmo 3092 . . 3
87albii 1620 . 2
9 df-disj 4424 . 2 Disj
10 df-disj 4424 . 2 Disj
118, 9, 103bitr4i 277 1 Disj Disj
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184  wal 1377   wceq 1379   wcel 1767  wnfc 2615  wrmo 2820  Disj wdisj 4423 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-mo 2280  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ral 2822  df-rex 2823  df-reu 2824  df-rmo 2825  df-disj 4424 This theorem is referenced by:  cbvdisjv  4434  disjors  4439  disjxiun  4450  volfiniun  21825  voliun  21832
 Copyright terms: Public domain W3C validator