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Theorem bj-dvdemo1 31461
Description: Remove dependency on ax-13 2101 from dvdemo1 4648 (this removal is noteworthy since dvdemo1 4648 and dvdemo2 4649 illustrate the phenomenon of bundling). (Contributed by BJ, 16-Jul-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-dvdemo1  |-  E. x
( x  =  y  ->  z  e.  x
)
Distinct variable group:    x, y

Proof of Theorem bj-dvdemo1
StepHypRef Expression
1 bj-dtru 31456 . . 3  |-  -.  A. x  x  =  y
2 exnal 1709 . . 3  |-  ( E. x  -.  x  =  y  <->  -.  A. x  x  =  y )
31, 2mpbir 214 . 2  |-  E. x  -.  x  =  y
4 pm2.21 112 . 2  |-  ( -.  x  =  y  -> 
( x  =  y  ->  z  e.  x
) )
53, 4eximii 1719 1  |-  E. x
( x  =  y  ->  z  e.  x
)
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> 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-5 1768  ax-6 1815  ax-7 1861  ax-8 1899  ax-9 1906  ax-10 1925  ax-11 1930  ax-12 1943  ax-nul 4547  ax-pow 4594
This theorem depends on definitions:  df-bi 190  df-an 377  df-tru 1457  df-ex 1674  df-nf 1678
This theorem is referenced by: (None)
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