Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  ralidm Structured version   Unicode version

Theorem ralidm 3876
 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 3874 . . 3
2 rzal 3874 . . 3
31, 22thd 240 . 2
4 neq0 3748 . . 3
5 biimt 333 . . . 4
6 df-ral 2758 . . . . 5
7 nfra1 2784 . . . . . 6
8719.23 1938 . . . . 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  wal 1403   wceq 1405  wex 1633   wcel 1842  wral 2753  c0 3737 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380 This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ne 2600  df-ral 2758  df-v 3060  df-dif 3416  df-nul 3738 This theorem is referenced by:  issref  5322  cnvpo  5483  dfwe2  6555
 Copyright terms: Public domain W3C validator