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Theorem nfra2xy 2414
Description: Not-free given two restricted quantifiers. (Contributed by Jim Kingdon, 20-Aug-2018.)
Assertion
Ref Expression
nfra2xy  |-  F/ y A. x  e.  A  A. y  e.  B  ph
Distinct variable groups:    x, y    y, A
Allowed substitution hints:    ph( x, y)    A( x)    B( x, y)

Proof of Theorem nfra2xy
StepHypRef Expression
1 nfcv 2225 . 2  |-  F/_ y A
2 nfra1 2405 . 2  |-  F/ y A. y  e.  B  ph
31, 2nfralxy 2410 1  |-  F/ y A. x  e.  A  A. y  e.  B  ph
Colors of variables: wff set class
Syntax hints:   F/wnf 1392   A.wral 2355
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 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-4 1443  ax-17 1462  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-cleq 2078  df-clel 2081  df-nfc 2214  df-ral 2360
This theorem is referenced by:  invdisj  3815  reusv3  4256
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