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Theorem nfdisj1 4198
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 4186 . 2  |-  (Disj  x  e.  A B  <->  A. y E* x  e.  A
y  e.  B )
2 nfrmo1 2881 . . 3  |-  F/ x E* x  e.  A
y  e.  B
32nfal 1865 . 2  |-  F/ x A. y E* x  e.  A y  e.  B
41, 3nfxfr 1580 1  |-  F/ xDisj  x  e.  A B
Colors of variables: wff set class
Syntax hints:   A.wal 1550   F/wnf 1554    e. wcel 1726   E*wrmo 2710  Disj wdisj 4185
This theorem is referenced by:  disjabrex  24029  disjabrexf  24030  hasheuni  24480  measvunilem  24571  measvunilem0  24572  measvuni  24573  measinblem  24579  voliune  24590  volfiniune  24591  volmeas  24592  dstrvprob  24734
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762
This theorem depends on definitions:  df-bi 179  df-ex 1552  df-nf 1555  df-eu 2287  df-mo 2288  df-rmo 2715  df-disj 4186
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