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Theorem 4exdistr 1864
 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 630 . . . . . . . 8
21exbii 1572 . . . . . . 7
3 19.42v 1858 . . . . . . . 8
4 19.42v 1858 . . . . . . . . 9
54anbi2i 675 . . . . . . . 8
6 19.42v 1858 . . . . . . . . . 10
76anbi2i 675 . . . . . . . . 9
87anbi2i 675 . . . . . . . 8
93, 5, 83bitri 262 . . . . . . 7
102, 9bitri 240 . . . . . 6
1110exbii 1572 . . . . 5
12 19.42v 1858 . . . . 5
13 19.42v 1858 . . . . . 6
1413anbi2i 675 . . . . 5
1511, 12, 143bitri 262 . . . 4
1615exbii 1572 . . 3
17 19.42v 1858 . . 3
1816, 17bitri 240 . 2
1918exbii 1572 1
 Colors of variables: wff set class Syntax hints:   wb 176   wa 358  wex 1531 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-11 1727 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-nf 1535
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