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Theorem nfdisj1 3786
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 3774 . 2  |-  (Disj  x  e.  A  B  <->  A. y E* x  e.  A  y  e.  B )
2 nfrmo1 2499 . . 3  |-  F/ x E* x  e.  A  y  e.  B
32nfal 1484 . 2  |-  F/ x A. y E* x  e.  A  y  e.  B
41, 3nfxfr 1379 1  |-  F/ xDisj  x  e.  A  B
Colors of variables: wff set class
Syntax hints:   A.wal 1257   F/wnf 1365    e. wcel 1409   E*wrmo 2326  Disj wdisj 3773
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-4 1416  ax-ial 1443  ax-i5r 1444
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-eu 1919  df-mo 1920  df-rmo 2331  df-disj 3774
This theorem is referenced by: (None)
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