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Theorem nfra2xy 2381
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 2194 . 2  |-  F/_ y A
2 nfra1 2372 . 2  |-  F/ y A. y  e.  B  ph
31, 2nfralxy 2377 1  |-  F/ y A. x  e.  A  A. y  e.  B  ph
Colors of variables: wff set class
Syntax hints:   F/wnf 1365   A.wral 2323
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-4 1416  ax-17 1435  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ral 2328
This theorem is referenced by:  invdisj  3787  reusv3  4220
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