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Theorem nfra2xy 2519
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 2319 . 2 𝑦𝐴
2 nfra1 2508 . 2 𝑦𝑦𝐵 𝜑
31, 2nfralxy 2515 1 𝑦𝑥𝐴𝑦𝐵 𝜑
Colors of variables: wff set class
Syntax hints:  wnf 1460  wral 2455
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-17 1526  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-cleq 2170  df-clel 2173  df-nfc 2308  df-ral 2460
This theorem is referenced by:  invdisj  3999  reusv3  4462
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