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Theorem nfdisj1 3758
 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 3746 . 2 (Disj 𝑥𝐴 𝐵 ↔ ∀𝑦∃*𝑥𝐴 𝑦𝐵)
2 nfrmo1 2482 . . 3 𝑥∃*𝑥𝐴 𝑦𝐵
32nfal 1468 . 2 𝑥𝑦∃*𝑥𝐴 𝑦𝐵
41, 3nfxfr 1363 1 𝑥Disj 𝑥𝐴 𝐵
 Colors of variables: wff set class Syntax hints:  ∀wal 1241  Ⅎwnf 1349   ∈ wcel 1393  ∃*wrmo 2309  Disj wdisj 3745 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-ial 1427  ax-i5r 1428 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-eu 1903  df-mo 1904  df-rmo 2314  df-disj 3746 This theorem is referenced by: (None)
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