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Theorem wl-ax11-lem7 28547
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 1839 . 2  |-  F/ x  -.  A. x  x  =  y
2119.28 1859 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 184    /\ wa 369   A.wal 1368
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
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  28548
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