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Theorem rgen2w 2533
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 2532 . 2  |-  A. y  e.  B  ph
32rgenw 2532 1  |-  A. x  e.  A  A. y  e.  B  ph
Colors of variables: wff set class
Syntax hints:   A.wral 2455
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-gen 1449
This theorem depends on definitions:  df-bi 117  df-ral 2460
This theorem is referenced by:  fnmpoi  6204  ixxf  9896  fzf  10010  rexfiuz  10993  eltx  13652  txcnp  13664  txcnmpt  13666  txrest  13669  txlm  13672
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