Theorem nfra2xy 2536

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 2336	. 2 |- F/_ y A
2		nfra1 2525	. 2 |- F/ y A. y e. B ph
3	1, 2	nfralxy 2532	1 |- F/ y A. x e. A A. y e. B ph

Syntax hints:   F/wnf 1471   A.wral 2472

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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-17 1537  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-cleq 2186  df-clel 2189  df-nfc 2325  df-ral 2477

This theorem is referenced by:  invdisj  4023  reusv3  4491