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Theorem 4exdistr 1935
 Description: Distribution of existential quantifiers. (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 1929 . . . . 5
21anbi2i 677 . . . 4
3 19.42v 1929 . . . 4
4 df-3an 939 . . . 4
52, 3, 43bitr4i 270 . . 3
653exbii 1595 . 2
7 3exdistr 1934 . 2
86, 7bitri 242 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360   w3a 937  wex 1551 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-11 1762 This theorem depends on definitions:  df-bi 179  df-an 362  df-3an 939  df-ex 1552  df-nf 1555
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