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Theorem raldifeq 3917
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:   ,   ,

Proof of Theorem raldifeq
StepHypRef Expression
1 raldifeq.2 . . . 4
21biantrud 507 . . 3
3 ralunb 3684 . . 3
42, 3syl6bbr 263 . 2
5 raldifeq.1 . . . 4
6 undif 3908 . . . 4
75, 6sylib 196 . . 3
87raleqdv 3060 . 2
94, 8bitrd 253 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  A.wral 2807  \cdif 3472  u.cun 3473  C_wss 3475
This theorem is referenced by:  cantnfrescl  8116  rrxmet  21835
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785
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