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Theorem dveeq1 2103
Description: Quantifier introduction when one pair of variables is distinct. (Contributed by NM, 2-Jan-2002.) Remove dependency on ax-11 1896. (Revised by Wolf Lammen, 8-Sep-2018.)
Assertion
Ref Expression
dveeq1  |-  ( -. 
A. x  x  =  y  ->  ( y  =  z  ->  A. x  y  =  z )
)
Distinct variable group:    x, z

Proof of Theorem dveeq1
StepHypRef Expression
1 nfeqf1 2102 . 2  |-  ( -. 
A. x  x  =  y  ->  F/ x  y  =  z )
21nfrd 1930 1  |-  ( -. 
A. x  x  =  y  ->  ( y  =  z  ->  A. x  y  =  z )
)
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1435
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-12 1909  ax-13 2057
This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1658  df-nf 1662
This theorem is referenced by:  nfeqf  2104  axc11nlemOLD  2107  axc11n  2108  axc11nOLD  2109
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