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Theorem spsbbi 2030
Description: Specialization of biconditional. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
spsbbi  |-  ( A. x ( ph  <->  ps )  ->  ( [ y  /  x ] ph  <->  [ y  /  x ] ps )
)

Proof of Theorem spsbbi
StepHypRef Expression
1 stdpc4 1977 . 2  |-  ( A. x ( ph  <->  ps )  ->  [ y  /  x ] ( ph  <->  ps )
)
2 sbbi 2024 . 2  |-  ( [ y  /  x ]
( ph  <->  ps )  <->  ( [
y  /  x ] ph 
<->  [ y  /  x ] ps ) )
31, 2sylib 188 1  |-  ( A. x ( ph  <->  ps )  ->  ( [ y  /  x ] ph  <->  [ y  /  x ] ps )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   A.wal 1530   [wsb 1638
This theorem is referenced by:  sbbid  2031  sbco3  2041
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639
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