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Theorem nfra2xy 2452
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 2258 . 2 𝑦𝐴
2 nfra1 2443 . 2 𝑦𝑦𝐵 𝜑
31, 2nfralxy 2448 1 𝑦𝑥𝐴𝑦𝐵 𝜑
Colors of variables: wff set class
Syntax hints:  wnf 1421  wral 2393
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 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-4 1472  ax-17 1491  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-cleq 2110  df-clel 2113  df-nfc 2247  df-ral 2398
This theorem is referenced by:  invdisj  3893  reusv3  4351
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