Theorem nfra2xy 2586

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 2386	. 2 |- F/_ y A
2		nfra1 2575	. 2 |- F/ y A. y e. B ph
3	1, 2	nfralxy 2582	1 |- F/ y A. x e. A A. y e. B ph

Syntax hints:   F/wnf 1509   A.wral 2522

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 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-4 1559  ax-17 1575  ax-ial 1583  ax-i5r 1584  ax-ext 2216

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-cleq 2227  df-clel 2230  df-nfc 2375  df-ral 2527

This theorem is referenced by:  invdisj  4104  reusv3  4583