Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  nfdisj Unicode version

Theorem nfdisj 4434
 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

Proof of Theorem nfdisj
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfdisj2 4424 . 2
2 nftru 1626 . . . . 5
3 nfcvf 2644 . . . . . . . 8
4 nfdisj.1 . . . . . . . . 9
54a1i 11 . . . . . . . 8
63, 5nfeld 2627 . . . . . . 7
7 nfdisj.2 . . . . . . . . 9
87nfcri 2612 . . . . . . . 8
98a1i 11 . . . . . . 7
106, 9nfand 1925 . . . . . 6
1110adantl 466 . . . . 5
122, 11nfmod2 2297 . . . 4
1312trud 1404 . . 3
1413nfal 1947 . 2
151, 14nfxfr 1645 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  /\wa 369  A.wal 1393   wtru 1396  F/wnf 1616  e.wcel 1818  E*wmo 2283  F/_wnfc 2605  Disj_wdisj 4422 This theorem is referenced by:  disjxiun  4449 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rmo 2815  df-disj 4423
 Copyright terms: Public domain W3C validator