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Theorem wl-ax11-lem7 31829
Description: Lemma. (Contributed by Wolf Lammen, 30-Jun-2019.)
Assertion
Ref Expression
wl-ax11-lem7  |-  ( A. x ( -.  A. x  x  =  y  /\  ph )  <->  ( -.  A. x  x  =  y  /\  A. x ph ) )

Proof of Theorem wl-ax11-lem7
StepHypRef Expression
1 nfna1 1957 . 2  |-  F/ x  -.  A. x  x  =  y
2119.28 1979 1  |-  ( A. x ( -.  A. x  x  =  y  /\  ph )  <->  ( -.  A. x  x  =  y  /\  A. x ph ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 187    /\ wa 370   A.wal 1435
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 1838  ax-10 1886  ax-12 1904
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  31830
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