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Theorem wl-naev 30222
Description: If some set variables can assume different values, then any two distinct set variables cannot always be the same. (Contributed by Wolf Lammen, 10-Aug-2019.)
Assertion
Ref Expression
wl-naev  |-  ( -. 
A. x  x  =  y  ->  -.  A. u  u  =  v )
Distinct variable group:    v, u

Proof of Theorem wl-naev
StepHypRef Expression
1 aev 1948 . 2  |-  ( A. u  u  =  v  ->  A. x  x  =  y )
21con3i 135 1  |-  ( -. 
A. x  x  =  y  ->  -.  A. u  u  =  v )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1396
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-12 1859
This theorem depends on definitions:  df-bi 185  df-ex 1618
This theorem is referenced by:  wl-sbcom2d-lem2  30250  wl-sbal1  30253  wl-sbal2  30254  wl-ax11-lem3  30267
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