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Theorem rgen2w 2420
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 𝜑
Assertion
Ref Expression
rgen2w 𝑥𝐴𝑦𝐵 𝜑

Proof of Theorem rgen2w
StepHypRef Expression
1 rgenw.1 . . 3 𝜑
21rgenw 2419 . 2 𝑦𝐵 𝜑
32rgenw 2419 1 𝑥𝐴𝑦𝐵 𝜑
Colors of variables: wff set class
Syntax hints:  wral 2349
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 1379
This theorem depends on definitions:  df-bi 115  df-ral 2354
This theorem is referenced by:  fnmpt2i  5861  ixxf  8997  fzf  9109  rexfiuz  10013
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