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Theorem ralidm 3349
 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 nfra1 2372 . . 3
2 anidm 382 . . . 4
3 rsp2 2388 . . . 4
42, 3syl5bir 146 . . 3
51, 4ralrimi 2407 . 2
6 ax-1 5 . . . 4
7 nfra1 2372 . . . . 5
8719.23 1584 . . . 4
96, 8sylibr 141 . . 3
10 df-ral 2328 . . 3
119, 10sylibr 141 . 2
125, 11impbii 121 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 101   wb 102  wal 1257  wex 1397   wcel 1409  wral 2323 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-4 1416  ax-ial 1443  ax-i5r 1444 This theorem depends on definitions:  df-bi 114  df-nf 1366  df-ral 2328 This theorem is referenced by:  issref  4735  cnvpom  4888
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