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Theorem wl-ax11-lem4 31832
Description: Lemma. (Contributed by Wolf Lammen, 30-Jun-2019.)
Assertion
Ref Expression
wl-ax11-lem4  |-  F/ x
( A. u  u  =  y  /\  -.  A. x  x  =  y )
Distinct variable group:    x, u

Proof of Theorem wl-ax11-lem4
StepHypRef Expression
1 ancom 451 . 2  |-  ( ( A. u  u  =  y  /\  -.  A. x  x  =  y
)  <->  ( -.  A. x  x  =  y  /\  A. u  u  =  y ) )
2 nfna1 1958 . . 3  |-  F/ x  -.  A. x  x  =  y
3 wl-ax11-lem3 31831 . . 3  |-  ( -. 
A. x  x  =  y  ->  F/ x A. u  u  =  y )
42, 3nfan1 1983 . 2  |-  F/ x
( -.  A. x  x  =  y  /\  A. u  u  =  y )
51, 4nfxfr 1692 1  |-  F/ x
( A. u  u  =  y  /\  -.  A. x  x  =  y )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    /\ wa 370   A.wal 1435   F/wnf 1663
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-10 1887  ax-12 1905  ax-13 2053  ax-wl-11v 31828
This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1660  df-nf 1664
This theorem is referenced by:  wl-ax11-lem8  31836
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