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Theorem nfdisj1 3785
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 3773 . 2 (Disj 𝑥𝐴 𝐵 ↔ ∀𝑦∃*𝑥𝐴 𝑦𝐵)
2 nfrmo1 2499 . . 3 𝑥∃*𝑥𝐴 𝑦𝐵
32nfal 1484 . 2 𝑥𝑦∃*𝑥𝐴 𝑦𝐵
41, 3nfxfr 1379 1 𝑥Disj 𝑥𝐴 𝐵
Colors of variables: wff set class
Syntax hints:  wal 1257  wnf 1365  wcel 1409  ∃*wrmo 2326  Disj wdisj 3772
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-4 1416  ax-ial 1443  ax-i5r 1444
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-eu 1919  df-mo 1920  df-rmo 2331  df-disj 3773
This theorem is referenced by: (None)
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