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Theorem nfdisj1 3887
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 3875 . 2 (Disj 𝑥𝐴 𝐵 ↔ ∀𝑦∃*𝑥𝐴 𝑦𝐵)
2 nfrmo1 2578 . . 3 𝑥∃*𝑥𝐴 𝑦𝐵
32nfal 1538 . 2 𝑥𝑦∃*𝑥𝐴 𝑦𝐵
41, 3nfxfr 1433 1 𝑥Disj 𝑥𝐴 𝐵
Colors of variables: wff set class
Syntax hints:  wal 1312  wnf 1419  wcel 1463  ∃*wrmo 2394  Disj wdisj 3874
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-4 1470  ax-ial 1497  ax-i5r 1498
This theorem depends on definitions:  df-bi 116  df-nf 1420  df-eu 1978  df-mo 1979  df-rmo 2399  df-disj 3875
This theorem is referenced by: (None)
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