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Theorem rgen2w 2394
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
StepHypRef Expression
1 rgenw.1 . . 3  |-  ph
21rgenw 2393 . 2  |-  A. y  e.  B  ph
32rgenw 2393 1  |-  A. x  e.  A  A. y  e.  B  ph
Colors of variables: wff set class
Syntax hints:   A.wral 2323
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-gen 1354
This theorem depends on definitions:  df-bi 114  df-ral 2328
This theorem is referenced by:  fnmpt2i  5858  ixxf  8868  fzf  8980  rexfiuz  9816
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