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Theorem nfdisj1 4561
Description: Bound-variable hypothesis builder for disjoint collection. (Contributed by Mario Carneiro, 14-Nov-2016.)
Assertion
Ref Expression
nfdisj1 𝑥Disj 𝑥𝐴 𝐵

Proof of Theorem nfdisj1
Dummy variable 𝑦 is distinct from all other variables.
StepHypRef Expression
1 df-disj 4549 . 2 (Disj 𝑥𝐴 𝐵 ↔ ∀𝑦∃*𝑥𝐴 𝑦𝐵)
2 nfrmo1 3090 . . 3 𝑥∃*𝑥𝐴 𝑦𝐵
32nfal 2139 . 2 𝑥𝑦∃*𝑥𝐴 𝑦𝐵
41, 3nfxfr 1771 1 𝑥Disj 𝑥𝐴 𝐵
Colors of variables: wff setvar class
Syntax hints:  wal 1473  wnf 1699  wcel 1977  ∃*wrmo 2899  Disj wdisj 4548
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034
This theorem depends on definitions:  df-bi 196  df-or 384  df-tru 1478  df-ex 1696  df-nf 1701  df-eu 2462  df-mo 2463  df-rmo 2904  df-disj 4549
This theorem is referenced by:  disjabrex  28571  disjabrexf  28572  hasheuni  29268  ldgenpisyslem1  29347  measvunilem  29396  measvunilem0  29397  measvuni  29398  measinblem  29404  voliune  29413  volfiniune  29414  volmeas  29415  dstrvprob  29654  ismeannd  39154
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