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Theorem spsbbi 2100
Description: Specialization of biconditional. (Contributed by NM, 2-Jun-1993.)
Assertion
Ref Expression
spsbbi  |-  ( A. x ( ph  <->  ps )  ->  ( [ y  /  x ] ph  <->  [ y  /  x ] ps )
)

Proof of Theorem spsbbi
StepHypRef Expression
1 stdpc4 2050 . 2  |-  ( A. x ( ph  <->  ps )  ->  [ y  /  x ] ( ph  <->  ps )
)
2 sbbi 2099 . 2  |-  ( [ y  /  x ]
( ph  <->  ps )  <->  ( [
y  /  x ] ph 
<->  [ y  /  x ] ps ) )
31, 2sylib 196 1  |-  ( A. x ( ph  <->  ps )  ->  ( [ y  /  x ] ph  <->  [ y  /  x ] ps )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184   A.wal 1368   [wsb 1701
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 1709  ax-7 1729  ax-10 1776  ax-12 1793  ax-13 1944
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-ex 1588  df-nf 1591  df-sb 1702
This theorem is referenced by:  sbbid  2101  sbco3OLD  2121  sbeqi  29096
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