Theorem rgen2w 2606

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 2605	. 2 |- A. y e. B ph
3	2	rgenw 2605	1 |- A. x e. A A. y e. B ph

This proof depends on syntax axioms:   A.wral 2528

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-gen 1502

This proof depends on definitions:  df-bi 117  df-ral 2533

This theorem is used by:  fnmpoi  6439  ixxf  10300  fzf  10415  rexfiuz  11755  prdsvallem  13621  eltx  15360  txcnp  15372  txcnmpt  15374  txrest  15377  txlm  15380