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Theorem nfdisj 4385
 Description: Bound-variable hypothesis builder for disjoint collection. (Contributed by Mario Carneiro, 14-Nov-2016.)
Hypotheses
Ref Expression
nfdisj.1
nfdisj.2
Assertion
Ref Expression
nfdisj Disj

Proof of Theorem nfdisj
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfdisj2 4375 . 2 Disj
2 nftru 1677 . . . . 5
3 nfcvf 2615 . . . . . . . 8
4 nfdisj.1 . . . . . . . . 9
54a1i 11 . . . . . . . 8
63, 5nfeld 2600 . . . . . . 7
7 nfdisj.2 . . . . . . . . 9
87nfcri 2586 . . . . . . . 8
98a1i 11 . . . . . . 7
106, 9nfand 2008 . . . . . 6
1110adantl 468 . . . . 5
122, 11nfmod2 2312 . . . 4
1312trud 1453 . . 3
1413nfal 2030 . 2
151, 14nfxfr 1696 1 Disj
 Colors of variables: wff setvar class Syntax hints:   wn 3   wa 371  wal 1442   wtru 1445  wnf 1667   wcel 1887  wmo 2300  wnfc 2579  Disj wdisj 4373 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-eu 2303  df-mo 2304  df-cleq 2444  df-clel 2447  df-nfc 2581  df-rmo 2745  df-disj 4374 This theorem is referenced by:  disjxiun  4399
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