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Theorem nfeqf1 2047
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 2045 . 2  |-  ( -. 
A. x  x  =  y  ->  F/ x  z  =  y )
2 equcom 1799 . . 3  |-  ( z  =  y  <->  y  =  z )
32nfbii 1649 . 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 1396   F/wnf 1621
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-12 1859  ax-13 2004
This theorem depends on definitions:  df-bi 185  df-an 369  df-ex 1618  df-nf 1622
This theorem is referenced by:  dveeq1  2048  sbal2  2207  nfeud2  2298  wl-mo2dnae  30259
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