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Theorem nfdisj 4194
 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 4184 . 2 Disj
2 nftru 1563 . . . . 5
3 nfcvf 2594 . . . . . . . 8
4 nfdisj.1 . . . . . . . . 9
54a1i 11 . . . . . . . 8
63, 5nfeld 2587 . . . . . . 7
7 nfdisj.2 . . . . . . . . 9
87nfcri 2566 . . . . . . . 8
98a1i 11 . . . . . . 7
106, 9nfand 1843 . . . . . 6
1110adantl 453 . . . . 5
122, 11nfmod2 2294 . . . 4
1312trud 1332 . . 3
1413nfal 1864 . 2
151, 14nfxfr 1579 1 Disj
 Colors of variables: wff set class Syntax hints:   wn 3   wa 359   wtru 1325  wal 1549  wnf 1553   wcel 1725  wmo 2282  wnfc 2559  Disj wdisj 4182 This theorem is referenced by:  disjxiun  4209 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-cleq 2429  df-clel 2432  df-nfc 2561  df-rmo 2713  df-disj 4183
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