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Theorem wl-ax11-lem5 31833
Description: Lemma. (Contributed by Wolf Lammen, 30-Jun-2019.)
Assertion
Ref Expression
wl-ax11-lem5  |-  ( A. u  u  =  y  ->  ( A. u [
u  /  y ]
ph 
<-> 
A. y ph )
)

Proof of Theorem wl-ax11-lem5
StepHypRef Expression
1 sbequ12r 2048 . . 3  |-  ( u  =  y  ->  ( [ u  /  y ] ph  <->  ph ) )
21sps 1916 . 2  |-  ( A. u  u  =  y  ->  ( [ u  / 
y ] ph  <->  ph ) )
32dral1 2122 1  |-  ( A. u  u  =  y  ->  ( A. u [
u  /  y ]
ph 
<-> 
A. y ph )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 187   A.wal 1435   [wsb 1786
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
This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1660  df-nf 1664  df-sb 1787
This theorem is referenced by:  wl-ax11-lem6  31834
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