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Theorem bj-cbvexiw 31315
Description: Change bound variable. This is to cbvexvw 1889 what cbvaliw 1859 is to cbvalvw 1888. [TODO: move after cbvalivw 1860]. (Contributed by BJ, 17-Mar-2020.)
Hypotheses
Ref Expression
bj-cbvexiw.1  |-  ( E. x E. y ps 
->  E. y ps )
bj-cbvexiw.2  |-  ( ph  ->  A. y ph )
bj-cbvexiw.3  |-  ( y  =  x  ->  ( ph  ->  ps ) )
Assertion
Ref Expression
bj-cbvexiw  |-  ( E. x ph  ->  E. y ps )
Distinct variable group:    x, y
Allowed substitution hints:    ph( x, y)    ps( x, y)

Proof of Theorem bj-cbvexiw
StepHypRef Expression
1 bj-cbvexiw.1 . 2  |-  ( E. x E. y ps 
->  E. y ps )
2 bj-cbvexiw.2 . . 3  |-  ( ph  ->  A. y ph )
3 bj-cbvexiw.3 . . 3  |-  ( y  =  x  ->  ( ph  ->  ps ) )
42, 3spimeh 1851 . 2  |-  ( ph  ->  E. y ps )
51, 4bj-exlime 31264 1  |-  ( E. x ph  ->  E. y ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1452   E.wex 1673
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692  ax-6 1815
This theorem depends on definitions:  df-bi 190  df-ex 1674
This theorem is referenced by:  bj-cbvexivw  31316  bj-cbvexw  31317
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