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Theorem nfra2xy 2364
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 2178 . 2 𝑦𝐴
2 nfra1 2355 . 2 𝑦𝑦𝐵 𝜑
31, 2nfralxy 2360 1 𝑦𝑥𝐴𝑦𝐵 𝜑
Colors of variables: wff set class
Syntax hints:  wnf 1349  wral 2306
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311
This theorem is referenced by:  invdisj  3759  reusv3  4192
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