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Theorem nfdisj1 4163
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 4151 . 2  |-  (Disj  x  e.  A B  <->  A. y E* x  e.  A
y  e.  B )
2 nfrmo1 2847 . . 3  |-  F/ x E* x  e.  A
y  e.  B
32nfal 1860 . 2  |-  F/ x A. y E* x  e.  A y  e.  B
41, 3nfxfr 1576 1  |-  F/ xDisj  x  e.  A B
Colors of variables: wff set class
Syntax hints:   A.wal 1546   F/wnf 1550    e. wcel 1721   E*wrmo 2677  Disj wdisj 4150
This theorem is referenced by:  disjabrex  23985  disjabrexf  23986  hasheuni  24436  measvunilem  24527  measvunilem0  24528  measvuni  24529  measinblem  24535  voliune  24546  volfiniune  24547  volmeas  24548  dstrvprob  24690
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757
This theorem depends on definitions:  df-bi 178  df-ex 1548  df-nf 1551  df-eu 2266  df-mo 2267  df-rmo 2682  df-disj 4151
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