Theorem nfra2xy 2364

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

Step	Hyp	Ref	Expression
1		nfcv 2178	. 2 |- F/_ y A
2		nfra1 2355	. 2 |- F/ y A. y e. B ph
3	1, 2	nfralxy 2360	1 |- F/ y A. x e. A A. y e. B ph

Syntax hints:   F/wnf 1349   A.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