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Theorem ralexim 2335
Description: Relationship between restricted universal and existential quantifiers. (Contributed by Jim Kingdon, 17-Aug-2018.)
Assertion
Ref Expression
ralexim  |-  ( A. x  e.  A  ph  ->  -. 
E. x  e.  A  -.  ph )

Proof of Theorem ralexim
StepHypRef Expression
1 rexnalim 2334 . 2  |-  ( E. x  e.  A  -.  ph 
->  -.  A. x  e.  A  ph )
21con2i 567 1  |-  ( A. x  e.  A  ph  ->  -. 
E. x  e.  A  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wral 2323   E.wrex 2324
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-5 1352  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-4 1416  ax-17 1435  ax-ial 1443
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-fal 1265  df-nf 1366  df-ral 2328  df-rex 2329
This theorem is referenced by: (None)
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