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Theorem 4exdistr 1848
 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:   ,   ,   ,   ,   ,   ,
Allowed substitution hints:   ()   (,)   (,,)   (,,,)

Proof of Theorem 4exdistr
StepHypRef Expression
1 19.42v 1842 . . . . 5
21anbi2i 708 . . . 4
3 19.42v 1842 . . . 4
4 df-3an 1009 . . . 4
52, 3, 43bitr4i 285 . . 3
653exbii 1728 . 2
7 3exdistr 1847 . 2
86, 7bitri 257 1
 Colors of variables: wff setvar class Syntax hints:   wb 189   wa 376   w3a 1007  wex 1671 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813 This theorem depends on definitions:  df-bi 190  df-an 378  df-3an 1009  df-ex 1672 This theorem is referenced by: (None)
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