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Theorem 4exdistr 1781
Description: Distribution of existential quantifiers in a quadruple conjunction. (Contributed by NM, 9-Mar-1995.) (Proof shortened by Wolf Lammen, 20-Jan-2018.)
Assertion
Ref Expression
4exdistr
Distinct variable groups:   ,   ,   ,   ,   ,   ,

Proof of Theorem 4exdistr
StepHypRef Expression
1 19.42v 1775 . . . . 5
21anbi2i 694 . . . 4
3 19.42v 1775 . . . 4
4 df-3an 975 . . . 4
52, 3, 43bitr4i 277 . . 3
653exbii 1669 . 2
7 3exdistr 1780 . 2
86, 7bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  /\wa 369  /\w3a 973  E.wex 1612
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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