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Theorem nfeqf1 2000
Description: An equation between setvar is free of any other setvar. (Contributed by Wolf Lammen, 10-Jun-2019.)
Assertion
Ref Expression
nfeqf1  |-  ( -. 
A. x  x  =  y  ->  F/ x  y  =  z )
Distinct variable group:    x, z

Proof of Theorem nfeqf1
StepHypRef Expression
1 nfeqf2 1998 . 2  |-  ( -. 
A. x  x  =  y  ->  F/ x  z  =  y )
2 equcom 1734 . . 3  |-  ( z  =  y  <->  y  =  z )
32nfbii 1615 . 2  |-  ( F/ x  z  =  y  <-> 
F/ x  y  =  z )
41, 3sylib 196 1  |-  ( -. 
A. x  x  =  y  ->  F/ x  y  =  z )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1368   F/wnf 1590
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-10 1777  ax-12 1794  ax-13 1952
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1588  df-nf 1591
This theorem is referenced by:  dveeq1  2001  sbal2  2180  nfeud2  2275  wl-mo2dnae  28535
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