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Theorem wl-sb6rft 31841
Description: A specialization of wl-equsal1t 31838. Closed form of sb6rf 2221. (Contributed by Wolf Lammen, 27-Jul-2019.)
Assertion
Ref Expression
wl-sb6rft  |-  ( F/ x ph  ->  ( ph 
<-> 
A. x ( x  =  y  ->  [ x  /  y ] ph ) ) )

Proof of Theorem wl-sb6rft
StepHypRef Expression
1 nfnf1 1958 . . 3  |-  F/ x F/ x ph
2 id 22 . . 3  |-  ( F/ x ph  ->  F/ x ph )
3 sbequ12r 2052 . . . 4  |-  ( x  =  y  ->  ( [ x  /  y ] ph  <->  ph ) )
43a1i 11 . . 3  |-  ( F/ x ph  ->  (
x  =  y  -> 
( [ x  / 
y ] ph  <->  ph ) ) )
51, 2, 4wl-equsald 31836 . 2  |-  ( F/ x ph  ->  ( A. x ( x  =  y  ->  [ x  /  y ] ph ) 
<-> 
ph ) )
65bicomd 204 1  |-  ( F/ x ph  ->  ( ph 
<-> 
A. x ( x  =  y  ->  [ x  /  y ] ph ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 187   A.wal 1435   F/wnf 1661   [wsb 1790
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-12 1909  ax-13 2057
This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1658  df-nf 1662  df-sb 1791
This theorem is referenced by: (None)
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