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Theorem 3exdistr 1780
Description: Distribution of existential quantifiers in a triple conjunction. (Contributed by NM, 9-Mar-1995.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Assertion
Ref Expression
3exdistr
Distinct variable groups:   ,   ,   ,

Proof of Theorem 3exdistr
StepHypRef Expression
1 3anass 977 . . . 4
212exbii 1668 . . 3
3 19.42vv 1777 . . 3
4 exdistr 1776 . . . 4
54anbi2i 694 . . 3
62, 3, 53bitri 271 . 2
76exbii 1667 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  /\wa 369  /\w3a 973  E.wex 1612
This theorem is referenced by:  4exdistr  1781
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  ax-6 1747
This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-ex 1613
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