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Theorem nfra2xy 2506
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 2306 . 2 𝑦𝐴
2 nfra1 2495 . 2 𝑦𝑦𝐵 𝜑
31, 2nfralxy 2502 1 𝑦𝑥𝐴𝑦𝐵 𝜑
Colors of variables: wff set class
Syntax hints:  wnf 1447  wral 2442
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 1434  ax-7 1435  ax-gen 1436  ax-ie1 1480  ax-ie2 1481  ax-4 1497  ax-17 1513  ax-ial 1521  ax-i5r 1522  ax-ext 2146
This theorem depends on definitions:  df-bi 116  df-tru 1345  df-nf 1448  df-cleq 2157  df-clel 2160  df-nfc 2295  df-ral 2447
This theorem is referenced by:  invdisj  3971  reusv3  4433
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