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Theorem ralcom4 2576
 Description: Commutation of restricted and unrestricted universal quantifiers. (Contributed by NM, 26-Mar-2004.) (Proof shortened by Andrew Salmon, 8-Jun-2011.)
Assertion
Ref Expression
ralcom4
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   ()

Proof of Theorem ralcom4
StepHypRef Expression
1 ralcom 2473 . 2
2 ralv 2571 . . 3
32ralbii 2330 . 2
4 ralv 2571 . 2
51, 3, 43bitr3i 199 1
 Colors of variables: wff set class Syntax hints:   wb 98  wal 1241  wral 2306  cvv 2557 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-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-v 2559 This theorem is referenced by:  uniiunlem  3028  uni0b  3605  iunss  3698  trint  3869  reliun  4458  funimass4  5224  ralrnmpt2  5615
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