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Theorem rgen2a 2369
Description: Generalization rule for restricted quantification. Note that and needn't be distinct (and illustrates the use of dvelimor 1891). (Contributed by NM, 23-Nov-1994.) (Proof rewritten by Jim Kingdon, 1-Jun-2018.)
Hypothesis
Ref Expression
rgen2a.1
Assertion
Ref Expression
rgen2a
Distinct variable group:   ,
Allowed substitution hints:   (,)   ()

Proof of Theorem rgen2a
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfv 1418 . . . . 5  F/
2 eleq1 2097 . . . . 5
31, 2dvelimor 1891 . . . 4  F/
4 eleq1 2097 . . . . . . . . 9
5 rgen2a.1 . . . . . . . . . 10
65ex 108 . . . . . . . . 9
74, 6syl6bi 152 . . . . . . . 8
87pm2.43d 44 . . . . . . 7
98alimi 1341 . . . . . 6
109a1d 22 . . . . 5
11 nfr 1408 . . . . . 6  F/
126alimi 1341 . . . . . 6
1311, 12syl6 29 . . . . 5  F/
1410, 13jaoi 635 . . . 4  F/
153, 14ax-mp 7 . . 3
16 df-ral 2305 . . 3
1715, 16sylibr 137 . 2
1817rgen 2368 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wo 628  wal 1240   wceq 1242   F/wnf 1346   wcel 1390  wral 2300
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-cleq 2030  df-clel 2033  df-ral 2305
This theorem is referenced by:  ordsucunielexmid  4216  isoid  5393  issmo  5844  ecopover  6140  ecopoverg  6143  subf  7010  cnref1o  8357  ioof  8610  fzof  8771
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