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Theorem ralidm 3933
Description: Idempotent law for restricted quantifier. (Contributed by NM, 28-Mar-1997.)
Assertion
Ref Expression
ralidm
Distinct variable group:   ,

Proof of Theorem ralidm
StepHypRef Expression
1 rzal 3931 . . 3
2 rzal 3931 . . 3
31, 22thd 240 . 2
4 neq0 3795 . . 3
5 biimt 335 . . . 4
6 df-ral 2812 . . . . 5
7 nfra1 2838 . . . . . 6
8719.23 1910 . . . . 5
96, 8bitri 249 . . . 4
105, 9syl6rbbr 264 . . 3
114, 10sylbi 195 . 2
123, 11pm2.61i 164 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184  A.wal 1393  =wceq 1395  E.wex 1612  e.wcel 1818  A.wral 2807   c0 3784
This theorem is referenced by:  issref  5385  cnvpo  5550  dfwe2  6617
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-v 3111  df-dif 3478  df-nul 3785
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