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Theorem ralidm 3723
 Description: Idempotent law for restricted quantifier. (Contributed by NM, 28-Mar-1997.)
Assertion
Ref Expression
ralidm
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem ralidm
StepHypRef Expression
1 rzal 3721 . . 3
2 rzal 3721 . . 3
31, 22thd 232 . 2
4 neq0 3630 . . 3
5 biimt 326 . . . 4
6 df-ral 2702 . . . . 5
7 nfra1 2748 . . . . . 6
8719.23 1819 . . . . 5
96, 8bitri 241 . . . 4
105, 9syl6rbbr 256 . . 3
114, 10sylbi 188 . 2
123, 11pm2.61i 158 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177  wal 1549  wex 1550   wceq 1652   wcel 1725  wral 2697  c0 3620 This theorem is referenced by:  dfwe2  4754  issref  5239  cnvpo  5402 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-v 2950  df-dif 3315  df-nul 3621
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