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Theorem rspc2gv 2796
 Description: Restricted specialization with two quantifiers, using implicit substitution. (Contributed by BJ, 2-Dec-2021.)
Hypothesis
Ref Expression
rspc2gv.1
Assertion
Ref Expression
rspc2gv
Distinct variable groups:   ,,   ,,   ,,   ,,   ,,
Allowed substitution hints:   (,)

Proof of Theorem rspc2gv
StepHypRef Expression
1 df-ral 2419 . 2
2 df-ral 2419 . . . . 5
32imbi2i 225 . . . 4
43albii 1446 . . 3
5 19.21v 1845 . . . . . 6
65bicomi 131 . . . . 5
76albii 1446 . . . 4
8 impexp 261 . . . . . . 7
9 eleq1 2200 . . . . . . . . 9
10 eleq1 2200 . . . . . . . . 9
119, 10bi2anan9 595 . . . . . . . 8
12 rspc2gv.1 . . . . . . . 8
1311, 12imbi12d 233 . . . . . . 7
148, 13syl5bbr 193 . . . . . 6
1514spc2gv 2771 . . . . 5
1615pm2.43a 51 . . . 4
177, 16syl5bi 151 . . 3
184, 17syl5bi 151 . 2
191, 18syl5bi 151 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104  wal 1329   wceq 1331   wcel 1480  wral 2414 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-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-ral 2419  df-v 2683 This theorem is referenced by:  difinfsnlem  6977  difinfsn  6978  seqvalcd  10225  seqovcd  10229  qtopbasss  12679
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