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Theorem raaan 3306
Description: Rearrange restricted quantifiers. (Contributed by NM, 26-Oct-2010.)
Hypotheses
Ref Expression
raaan.1  F/
raaan.2  F/
Assertion
Ref Expression
raaan
Distinct variable group:   ,,
Allowed substitution hints:   (,)   (,)

Proof of Theorem raaan
StepHypRef Expression
1 raaan.1 . . . 4  F/
2 raaan.2 . . . 4  F/
31, 2raaanlem 3305 . . 3
43pm5.74i 169 . 2
5 ralm 3304 . 2
6 jcab 522 . . 3
7 ralm 3304 . . . 4
8 eleq1 2082 . . . . . . 7
98cbvexv 1777 . . . . . 6
109imbi1i 227 . . . . 5
11 ralm 3304 . . . . 5
1210, 11bitri 173 . . . 4
137, 12anbi12i 436 . . 3
146, 13bitri 173 . 2
154, 5, 143bitr3i 199 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98   F/wnf 1329  wex 1362   wcel 1374  wral 2284
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 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-cleq 2015  df-clel 2018  df-nfc 2149  df-ral 2289
This theorem is referenced by:  raaanv  3307
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