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Theorem rgenz 3725
 Description: Generalization rule that eliminates a non-zero class requirement. (Contributed by NM, 8-Dec-2012.)
Hypothesis
Ref Expression
rgenz.1
Assertion
Ref Expression
rgenz
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem rgenz
StepHypRef Expression
1 rzal 3721 . 2
2 rgenz.1 . . 3
32ralrimiva 2781 . 2
41, 3pm2.61ine 2674 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wcel 1725   wne 2598  wral 2697  c0 3620 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-v 2950  df-dif 3315  df-nul 3621
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