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Theorem rgen2w 2465
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 2464 . 2  |-  A. y  e.  B  ph
32rgenw 2464 1  |-  A. x  e.  A  A. y  e.  B  ph
Colors of variables: wff set class
Syntax hints:   A.wral 2393
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-gen 1410
This theorem depends on definitions:  df-bi 116  df-ral 2398
This theorem is referenced by:  fnmpoi  6070  ixxf  9649  fzf  9762  rexfiuz  10729  eltx  12355  txcnp  12367  txcnmpt  12369  txrest  12372  txlm  12375
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