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Theorem r3al 2837
Description: Triple restricted universal quantification. (Contributed by NM, 19-Nov-1995.) (Proof shortened by Wolf Lammen, 30-Dec-2019.)
Assertion
Ref Expression
r3al
Distinct variable groups:   , ,   , ,   ,

Proof of Theorem r3al
StepHypRef Expression
1 r2al 2835 . 2
2 19.21v 1729 . . . 4
3 df-3an 975 . . . . . . 7
43imbi1i 325 . . . . . 6
5 impexp 446 . . . . . 6
64, 5bitri 249 . . . . 5
76albii 1640 . . . 4
8 df-ral 2812 . . . . 5
98imbi2i 312 . . . 4
102, 7, 93bitr4ri 278 . . 3
11102albii 1641 . 2
121, 11bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  /\w3a 973  A.wal 1393  e.wcel 1818  A.wral 2807
This theorem is referenced by:  pocl  4812  dfwe2  6617  isass  25318
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704
This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-ex 1613  df-ral 2812
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