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Theorem nfdisj1 3835
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 3823 . 2 (Disj 𝑥𝐴 𝐵 ↔ ∀𝑦∃*𝑥𝐴 𝑦𝐵)
2 nfrmo1 2539 . . 3 𝑥∃*𝑥𝐴 𝑦𝐵
32nfal 1513 . 2 𝑥𝑦∃*𝑥𝐴 𝑦𝐵
41, 3nfxfr 1408 1 𝑥Disj 𝑥𝐴 𝐵
Colors of variables: wff set class
Syntax hints:  wal 1287  wnf 1394  wcel 1438  ∃*wrmo 2362  Disj wdisj 3822
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-ial 1472  ax-i5r 1473
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-eu 1951  df-mo 1952  df-rmo 2367  df-disj 3823
This theorem is referenced by: (None)
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