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Theorem nfra2xy 2419
 Description: Not-free given two restricted quantifiers. (Contributed by Jim Kingdon, 20-Aug-2018.)
Assertion
Ref Expression
nfra2xy 𝑦𝑥𝐴𝑦𝐵 𝜑
Distinct variable groups:   𝑥,𝑦   𝑦,𝐴
Allowed substitution hints:   𝜑(𝑥,𝑦)   𝐴(𝑥)   𝐵(𝑥,𝑦)

Proof of Theorem nfra2xy
StepHypRef Expression
1 nfcv 2229 . 2 𝑦𝐴
2 nfra1 2410 . 2 𝑦𝑦𝐵 𝜑
31, 2nfralxy 2415 1 𝑦𝑥𝐴𝑦𝐵 𝜑
 Colors of variables: wff set class Syntax hints:  Ⅎwnf 1395  ∀wral 2360 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-4 1446  ax-17 1465  ax-ial 1473  ax-i5r 1474  ax-ext 2071 This theorem depends on definitions:  df-bi 116  df-tru 1293  df-nf 1396  df-cleq 2082  df-clel 2085  df-nfc 2218  df-ral 2365 This theorem is referenced by:  invdisj  3845  reusv3  4295
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