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Theorem rspc2gv 2720
 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 2358 . 2
2 df-ral 2358 . . . . 5
32imbi2i 224 . . . 4
43albii 1400 . . 3
5 19.21v 1796 . . . . . 6
65bicomi 130 . . . . 5
76albii 1400 . . . 4
8 impexp 259 . . . . . . 7
9 eleq1 2145 . . . . . . . . 9
10 eleq1 2145 . . . . . . . . 9
119, 10bi2anan9 571 . . . . . . . 8
12 rspc2gv.1 . . . . . . . 8
1311, 12imbi12d 232 . . . . . . 7
148, 13syl5bbr 192 . . . . . 6
1514spc2gv 2697 . . . . 5
1615pm2.43a 50 . . . 4
177, 16syl5bi 150 . . 3
184, 17syl5bi 150 . 2
191, 18syl5bi 150 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wb 103  wal 1283   wceq 1285   wcel 1434  wral 2353 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-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065 This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-ral 2358  df-v 2612 This theorem is referenced by: (None)
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