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Theorem dveel2ALT 2226
Description: Version of dveel2 2054 using ax-16 2179 instead of ax-17 1623. (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 2224 . 2  |-  ( z  e.  w  ->  A. x  z  e.  w )
2 ax17el 2224 . 2  |-  ( z  e.  y  ->  A. w  z  e.  y )
3 elequ2 1722 . 2  |-  ( w  =  y  ->  (
z  e.  w  <->  z  e.  y ) )
41, 2, 3dvelimh 2005 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 1546
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-14 1721  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-15 2178  ax-16 2179
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1548  df-nf 1551
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