Theorem rgen2w 2419

Description: Generalization rule for restricted quantification. Note that x and y needn't be distinct. (Contributed by NM, 18-Jun-2014.)

Hypothesis

Ref	Expression
rgenw.1	|- ph

Assertion

Ref	Expression
rgen2w	|- A. x e. A A. y e. B ph

Proof of Theorem rgen2w

Step	Hyp	Ref	Expression
1		rgenw.1	. . 3 |- ph
2	1	rgenw 2418	. 2 |- A. y e. B ph
3	2	rgenw 2418	1 |- A. x e. A A. y e. B ph

Syntax hints:   A.wral 2348

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-gen 1378

This theorem depends on definitions:  df-bi 115  df-ral 2353

This theorem is referenced by:  fnmpt2i  5850  ixxf  8921  fzf  9033  rexfiuz  9875