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Theorem nfdisj 4042
 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 df-disj 4031 . . 3 Disj
2 df-rmo 2585 . . . 4
32albii 1557 . . 3
41, 3bitri 240 . 2 Disj
5 nftru 1545 . . . . 5
6 nfcvf 2474 . . . . . . . 8
7 nfdisj.1 . . . . . . . . 9
87a1i 10 . . . . . . . 8
96, 8nfeld 2467 . . . . . . 7
10 nfdisj.2 . . . . . . . . 9
1110nfcri 2446 . . . . . . . 8
1211a1i 10 . . . . . . 7
139, 12nfand 1788 . . . . . 6
1413adantl 452 . . . . 5
155, 14nfmod2 2189 . . . 4
1615trud 1314 . . 3
1716nfal 1794 . 2
184, 17nfxfr 1561 1 Disj
 Colors of variables: wff set class Syntax hints:   wn 3   wa 358   wtru 1307  wal 1531  wnf 1535   wcel 1701  wmo 2177  wnfc 2439  wrmo 2580  Disj wdisj 4030 This theorem is referenced by:  disjxiun  4057 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1537  ax-5 1548  ax-17 1607  ax-9 1645  ax-8 1666  ax-6 1720  ax-7 1725  ax-11 1732  ax-12 1897  ax-ext 2297 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1533  df-nf 1536  df-sb 1640  df-eu 2180  df-mo 2181  df-cleq 2309  df-clel 2312  df-nfc 2441  df-rmo 2585  df-disj 4031
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