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Theorem nfdisj1 3841
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 3829 . 2  |-  (Disj  x  e.  A  B  <->  A. y E* x  e.  A  y  e.  B )
2 nfrmo1 2540 . . 3  |-  F/ x E* x  e.  A  y  e.  B
32nfal 1514 . 2  |-  F/ x A. y E* x  e.  A  y  e.  B
41, 3nfxfr 1409 1  |-  F/ xDisj  x  e.  A  B
Colors of variables: wff set class
Syntax hints:   A.wal 1288   F/wnf 1395    e. wcel 1439   E*wrmo 2363  Disj wdisj 3828
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-4 1446  ax-ial 1473  ax-i5r 1474
This theorem depends on definitions:  df-bi 116  df-nf 1396  df-eu 1952  df-mo 1953  df-rmo 2368  df-disj 3829
This theorem is referenced by: (None)
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