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Theorem nfra2xy 2407
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 2220 . 2 𝑦𝐴
2 nfra1 2398 . 2 𝑦𝑦𝐵 𝜑
31, 2nfralxy 2403 1 𝑦𝑥𝐴𝑦𝐵 𝜑
Colors of variables: wff set class
Syntax hints:  wnf 1390  wral 2349
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 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-17 1460  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354
This theorem is referenced by:  invdisj  3788  reusv3  4218
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