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Theorem bj-dvdemo2 31484
Description: Remove dependency on ax-13 2104 from dvdemo2 4636 (this removal is noteworthy since dvdemo1 4635 and dvdemo2 4636 illustrate the phenomenon of bundling). (Contributed by BJ, 16-Jul-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-dvdemo2  |-  E. x
( x  =  y  ->  z  e.  x
)
Distinct variable group:    x, z

Proof of Theorem bj-dvdemo2
StepHypRef Expression
1 bj-el 31477 . 2  |-  E. x  z  e.  x
2 ax-1 6 . 2  |-  ( z  e.  x  ->  (
x  =  y  -> 
z  e.  x ) )
31, 2eximii 1717 1  |-  E. x
( x  =  y  ->  z  e.  x
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   E.wex 1671
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-8 1906  ax-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-pow 4579
This theorem depends on definitions:  df-bi 190  df-an 378  df-ex 1672  df-nf 1676
This theorem is referenced by: (None)
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