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Theorem bj-hbsb3t 31253
Description: A theorem close to a closed form of hbsb3 2154. (Contributed by BJ, 2-May-2019.)
Assertion
Ref Expression
bj-hbsb3t  |-  ( A. x ( ph  ->  A. y ph )  -> 
( [ y  /  x ] ph  ->  A. x [ y  /  x ] ph ) )

Proof of Theorem bj-hbsb3t
StepHypRef Expression
1 spsbim 2186 . 2  |-  ( A. x ( ph  ->  A. y ph )  -> 
( [ y  /  x ] ph  ->  [ y  /  x ] A. y ph ) )
2 hbsb2a 2152 . 2  |-  ( [ y  /  x ] A. y ph  ->  A. x [ y  /  x ] ph )
31, 2syl6 34 1  |-  ( A. x ( ph  ->  A. y ph )  -> 
( [ y  /  x ] ph  ->  A. x [ y  /  x ] ph ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   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 1838  ax-10 1886  ax-12 1904  ax-13 2052
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:  bj-hbsb3  31254  bj-nfs1t  31255
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