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Theorem dveel2 2108
Description: Quantifier introduction when one pair of variables is distinct. (Contributed by NM, 2-Jan-2002.)
Assertion
Ref Expression
dveel2  |-  ( -. 
A. x  x  =  y  ->  ( z  e.  y  ->  A. x  z  e.  y )
)
Distinct variable group:    x, z

Proof of Theorem dveel2
Dummy variable  w is distinct from all other variables.
StepHypRef Expression
1 elequ2 1731 . 2  |-  ( w  =  y  ->  (
z  e.  w  <->  z  e.  y ) )
21dvelimv 2075 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 1550
This theorem is referenced by:  ax15  2109
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951
This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555
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