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Theorem ralidm 3653
 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 3651 . . 3
2 rzal 3651 . . 3
31, 22thd 231 . 2
4 neq0 3560 . . 3
5 biimt 325 . . . 4
6 df-ral 2619 . . . . 5
7 nfra1 2664 . . . . . 6
8719.23 1801 . . . . 5
96, 8bitri 240 . . . 4
105, 9syl6rbbr 255 . . 3
114, 10sylbi 187 . 2
123, 11pm2.61i 156 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 176  wal 1540  wex 1541   wceq 1642   wcel 1710  wral 2614  c0 3550 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-ral 2619  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-dif 3215  df-nul 3551 This theorem is referenced by: (None)
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