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Theorem dveel2ALT 2130
Description: Version of dveel2 1960 using ax-16 2083 instead of ax-17 1603. (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 2128 . 2  |-  ( z  e.  w  ->  A. x  z  e.  w )
2 ax17el 2128 . 2  |-  ( z  e.  y  ->  A. w  z  e.  y )
3 elequ2 1689 . 2  |-  ( w  =  y  ->  (
z  e.  w  <->  z  e.  y ) )
41, 2, 3dvelimh 1904 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 1527
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-15 2082  ax-16 2083
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529  df-nf 1532
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