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Theorem wl-ax11-lem4 28547
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 450 . 2  |-  ( ( A. u  u  =  y  /\  -.  A. x  x  =  y
)  <->  ( -.  A. x  x  =  y  /\  A. u  u  =  y ) )
2 nfna1 1841 . . 3  |-  F/ x  -.  A. x  x  =  y
3 wl-ax11-lem3 28546 . . 3  |-  ( -. 
A. x  x  =  y  ->  F/ x A. u  u  =  y )
42, 3nfan1 1864 . 2  |-  F/ x
( -.  A. x  x  =  y  /\  A. u  u  =  y )
51, 4nfxfr 1616 1  |-  F/ x
( A. u  u  =  y  /\  -.  A. x  x  =  y )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    /\ wa 369   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 1954  ax-wl-11v 28543
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1588  df-nf 1591
This theorem is referenced by:  wl-ax11-lem8  28551
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