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Theorem raldifeq 3863
 Description: Equality theorem for restricted universal quantifier. (Contributed by Thierry Arnoux, 6-Jul-2019.)
Hypotheses
Ref Expression
raldifeq.1
raldifeq.2
Assertion
Ref Expression
raldifeq
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem raldifeq
StepHypRef Expression
1 raldifeq.2 . . . 4
21biantrud 507 . . 3
3 ralunb 3626 . . 3
42, 3syl6bbr 265 . 2
5 raldifeq.1 . . . 4
6 undif 3854 . . . 4
75, 6sylib 198 . . 3
87raleqdv 3012 . 2
94, 8bitrd 255 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 186   wa 369   wceq 1407  wral 2756   cdif 3413   cun 3414   wss 3416 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1641  ax-4 1654  ax-5 1727  ax-6 1773  ax-7 1816  ax-10 1863  ax-11 1868  ax-12 1880  ax-13 2028  ax-ext 2382 This theorem depends on definitions:  df-bi 187  df-or 370  df-an 371  df-tru 1410  df-ex 1636  df-nf 1640  df-sb 1766  df-clab 2390  df-cleq 2396  df-clel 2399  df-nfc 2554  df-ne 2602  df-ral 2761  df-rab 2765  df-v 3063  df-dif 3419  df-un 3421  df-in 3423  df-ss 3430  df-nul 3741 This theorem is referenced by:  cantnfrescl  8129  rrxmet  22129
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