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Theorem nfdisj1 4022
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 4010 . 2  |-  (Disj  x  e.  A B  <->  A. y E* x  e.  A
y  e.  B )
2 nfrmo1 2724 . . 3  |-  F/ x E* x  e.  A
y  e.  B
32nfal 1778 . 2  |-  F/ x A. y E* x  e.  A y  e.  B
41, 3nfxfr 1560 1  |-  F/ xDisj  x  e.  A B
Colors of variables: wff set class
Syntax hints:   A.wal 1530   F/wnf 1534    e. wcel 1696   E*wrmo 2559  Disj wdisj 4009
This theorem is referenced by:  disjabrex  23374  disjabrexf  23375  hasheuni  23468  measvunilem  23555  measvunilem0  23556  measvuni  23557  measinblem  23562  dstrvprob  23687
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
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-eu 2160  df-mo 2161  df-rmo 2564  df-disj 4010
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