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Theorem 3exdistr 1934
 Description: Distribution of existential quantifiers. (Contributed by NM, 9-Mar-1995.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Assertion
Ref Expression
3exdistr
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   (,)   (,,)

Proof of Theorem 3exdistr
StepHypRef Expression
1 3anass 941 . . . 4
212exbii 1594 . . 3
3 19.42vv 1931 . . 3
4 exdistr 1930 . . . 4
54anbi2i 677 . . 3
62, 3, 53bitri 264 . 2
76exbii 1593 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360   w3a 937  wex 1551 This theorem is referenced by:  4exdistr  1935 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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