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Theorem r3al 2886
 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 2801 . 2
2 r2al 2871 . . 3
32ralbii 2836 . 2
4 3anass 969 . . . . . . . . 9
54imbi1i 325 . . . . . . . 8
6 impexp 446 . . . . . . . 8
75, 6bitri 249 . . . . . . 7
87albii 1611 . . . . . 6
9 19.21v 1920 . . . . . 6
108, 9bitri 249 . . . . 5
1110albii 1611 . . . 4
12 19.21v 1920 . . . 4
1311, 12bitri 249 . . 3
1413albii 1611 . 2
151, 3, 143bitr4i 277 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   w3a 965  wal 1368   wcel 1758  wral 2796 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1954  ax-ext 2431 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-ex 1588  df-nf 1591  df-sb 1703  df-cleq 2444  df-clel 2447  df-nfc 2602  df-ral 2801 This theorem is referenced by:  pocl  4751  dfwe2  6498  isass  23950
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