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Theorem r3al 2671
 Description: Triple restricted universal quantification. (Contributed by NM, 19-Nov-1995.)
Assertion
Ref Expression
r3al
Distinct variable groups:   ,,   ,,   ,
Allowed substitution hints:   (,,)   ()   (,)   (,,)

Proof of Theorem r3al
StepHypRef Expression
1 df-ral 2619 . 2
2 r2al 2651 . . 3
32ralbii 2638 . 2
4 3anass 938 . . . . . . . . 9
54imbi1i 315 . . . . . . . 8
6 impexp 433 . . . . . . . 8
75, 6bitri 240 . . . . . . 7
87albii 1566 . . . . . 6
9 19.21v 1890 . . . . . 6
108, 9bitri 240 . . . . 5
1110albii 1566 . . . 4
12 19.21v 1890 . . . 4
1311, 12bitri 240 . . 3
1413albii 1566 . 2
151, 3, 143bitr4i 268 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358   w3a 934  wal 1540   wcel 1710  wral 2614 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619 This theorem is referenced by: (None)
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