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Theorem nfdisj1 4401
Description: Bound-variable hypothesis builder for disjoint collection. (Contributed by Mario Carneiro, 14-Nov-2016.)
Assertion
Ref Expression
nfdisj1  |-  F/ xDisj  x  e.  A  B

Proof of Theorem nfdisj1
Dummy variable  y is distinct from all other variables.
StepHypRef Expression
1 df-disj 4389 . 2  |-  (Disj  x  e.  A  B  <->  A. y E* x  e.  A  y  e.  B )
2 nfrmo1 2998 . . 3  |-  F/ x E* x  e.  A  y  e.  B
32nfal 2002 . 2  |-  F/ x A. y E* x  e.  A  y  e.  B
41, 3nfxfr 1692 1  |-  F/ xDisj  x  e.  A  B
Colors of variables: wff setvar class
Syntax hints:   A.wal 1435   F/wnf 1663    e. wcel 1867   E*wrmo 2776  Disj wdisj 4388
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-10 1886  ax-11 1891  ax-12 1904
This theorem depends on definitions:  df-bi 188  df-ex 1660  df-nf 1664  df-eu 2267  df-mo 2268  df-rmo 2781  df-disj 4389
This theorem is referenced by:  disjabrex  28172  disjabrexf  28173  hasheuni  28895  ldgenpisyslem1  28974  measvunilem  29023  measvunilem0  29024  measvuni  29025  measinblem  29031  voliune  29041  volfiniune  29042  volmeas  29043  dstrvprob  29293  ismeannd  38035
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