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Theorem rababg 36179
 Description: Condition when restricted class is equal to unrestricted class. (Contributed by RP, 13-Aug-2020.)
Assertion
Ref Expression
rababg

Proof of Theorem rababg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ancrb 553 . . 3
21albii 1691 . 2
3 nfv 1761 . . 3
4 nfsab1 2441 . . . 4
5 nfrab1 2971 . . . . 5
65nfcri 2586 . . . 4
74, 6nfim 2003 . . 3
8 abid 2439 . . . . 5
9 eleq1 2517 . . . . 5
108, 9syl5bbr 263 . . . 4
11 rabid 2967 . . . . 5
12 eleq1 2517 . . . . 5
1311, 12syl5bbr 263 . . . 4
1410, 13imbi12d 322 . . 3
153, 7, 14cbval 2114 . 2
16 eqss 3447 . . 3
17 rabssab 3516 . . . 4
1817biantrur 509 . . 3
19 dfss2 3421 . . 3
2016, 18, 193bitr2ri 278 . 2
212, 15, 203bitri 275 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 188   wa 371  wal 1442   wceq 1444   wcel 1887  cab 2437  crab 2741   wss 3404 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-rab 2746  df-in 3411  df-ss 3418 This theorem is referenced by: (None)
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