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Theorem dveel2ALT 2247
Description: Alternate proof of dveel2 2069 using ax-c16 2201 instead of ax-5 1671. (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 ax5el 2245 . 2  |-  ( z  e.  w  ->  A. x  z  e.  w )
2 ax5el 2245 . 2  |-  ( z  e.  y  ->  A. w  z  e.  y )
3 elequ2 1763 . 2  |-  ( w  =  y  ->  (
z  e.  w  <->  z  e.  y ) )
41, 2, 3dvelimh 2035 1  |-  ( -. 
A. x  x  =  y  ->  ( z  e.  y  ->  A. x  z  e.  y )
)
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1368
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1952  ax-c14 2200  ax-c16 2201
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1588  df-nf 1591
This theorem is referenced by: (None)
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