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Theorem r3al 2765
 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 2712 . 2
2 r2al 2744 . . 3
32ralbii 2731 . 2
4 3anass 941 . . . . . . . . 9
54imbi1i 317 . . . . . . . 8
6 impexp 435 . . . . . . . 8
75, 6bitri 242 . . . . . . 7
87albii 1576 . . . . . 6
9 19.21v 1914 . . . . . 6
108, 9bitri 242 . . . . 5
1110albii 1576 . . . 4
12 19.21v 1914 . . . 4
1311, 12bitri 242 . . 3
1413albii 1576 . 2
151, 3, 143bitr4i 270 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   w3a 937  wal 1550   wcel 1726  wral 2707 This theorem is referenced by:  pocl  4513  dfwe2  4765  isass  21909 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712
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