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Theorem ralidm 3315
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 2349 . . 3  F/
2 anidm 376 . . . 4
3 rsp2 2365 . . . 4
42, 3syl5bir 142 . . 3
51, 4ralrimi 2384 . 2
6 ax-1 5 . . . 4
7 nfra1 2349 . . . . 5  F/
8719.23 1565 . . . 4
96, 8sylibr 137 . . 3
10 df-ral 2305 . . 3
119, 10sylibr 137 . 2
125, 11impbii 117 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  wal 1240  wex 1378   wcel 1390  wral 2300
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-ial 1424  ax-i5r 1425
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-ral 2305
This theorem is referenced by:  issref  4650  cnvpom  4803
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