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Theorem dveel2ALT 2143
Description: Version of dveel2 1973 using ax-16 2096 instead of ax-17 1606. (Contributed by NM, 10-May-2008.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
dveel2ALT  |-  ( -. 
A. x  x  =  y  ->  ( z  e.  y  ->  A. x  z  e.  y )
)
Distinct variable group:    x, z

Proof of Theorem dveel2ALT
Dummy variable  w is distinct from all other variables.
StepHypRef Expression
1 ax17el 2141 . 2  |-  ( z  e.  w  ->  A. x  z  e.  w )
2 ax17el 2141 . 2  |-  ( z  e.  y  ->  A. w  z  e.  y )
3 elequ2 1701 . 2  |-  ( w  =  y  ->  (
z  e.  w  <->  z  e.  y ) )
41, 2, 3dvelimh 1917 1  |-  ( -. 
A. x  x  =  y  ->  ( z  e.  y  ->  A. x  z  e.  y )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1530
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-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-15 2095  ax-16 2096
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-nf 1535
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