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Theorem wl-ax11-lem4 30271
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 448 . 2  |-  ( ( A. u  u  =  y  /\  -.  A. x  x  =  y
)  <->  ( -.  A. x  x  =  y  /\  A. u  u  =  y ) )
2 nfna1 1908 . . 3  |-  F/ x  -.  A. x  x  =  y
3 wl-ax11-lem3 30270 . . 3  |-  ( -. 
A. x  x  =  y  ->  F/ x A. u  u  =  y )
42, 3nfan1 1932 . 2  |-  F/ x
( -.  A. x  x  =  y  /\  A. u  u  =  y )
51, 4nfxfr 1650 1  |-  F/ x
( A. u  u  =  y  /\  -.  A. x  x  =  y )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    /\ wa 367   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  ax-wl-11v 30267
This theorem depends on definitions:  df-bi 185  df-an 369  df-ex 1618  df-nf 1622
This theorem is referenced by:  wl-ax11-lem8  30275
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