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Theorem 4exdistr 1793
 Description: Distribution of existential quantifiers. (Contributed by NM, 9-Mar-1995.)
Assertion
Ref Expression
4exdistr
Distinct variable groups:   ,   ,   ,   ,   ,   ,
Allowed substitution hints:   ()   (,)   (,,)   (,,,)

Proof of Theorem 4exdistr
StepHypRef Expression
1 anass 381 . . . . . . . 8
21exbii 1496 . . . . . . 7
3 19.42v 1786 . . . . . . . 8
4 19.42v 1786 . . . . . . . . 9
54anbi2i 430 . . . . . . . 8
6 19.42v 1786 . . . . . . . . . 10
76anbi2i 430 . . . . . . . . 9
87anbi2i 430 . . . . . . . 8
93, 5, 83bitri 195 . . . . . . 7
102, 9bitri 173 . . . . . 6
1110exbii 1496 . . . . 5
12 19.42v 1786 . . . . 5
13 19.42v 1786 . . . . . 6
1413anbi2i 430 . . . . 5
1511, 12, 143bitri 195 . . . 4
1615exbii 1496 . . 3
17 19.42v 1786 . . 3
1816, 17bitri 173 . 2
1918exbii 1496 1
 Colors of variables: wff set class Syntax hints:   wa 97   wb 98  wex 1381 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427 This theorem depends on definitions:  df-bi 110 This theorem is referenced by: (None)
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