Theorem nfra2xy 2475

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 2281	. 2 |- F/_ y A
2		nfra1 2466	. 2 |- F/ y A. y e. B ph
3	1, 2	nfralxy 2471	1 |- F/ y A. x e. A A. y e. B ph

Syntax hints:   F/wnf 1436   A.wral 2416

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-17 1506  ax-ial 1514  ax-i5r 1515  ax-ext 2121

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421

This theorem is referenced by:  invdisj  3923  reusv3  4381