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Theorem sbcbiiiOLD 26846
Description: Fully inferenced rewriting under an explicit substitution. (Contributed by Stefan O'Rear, 11-Oct-2014.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
sbcbiii.1  |-  A  e. 
_V
sbcbiii.2  |-  ( ph  <->  ps )
Assertion
Ref Expression
sbcbiiiOLD  |-  ( [. A  /  a ]. ph  <->  [. A  / 
a ]. ps )

Proof of Theorem sbcbiiiOLD
StepHypRef Expression
1 sbcbiii.2 . 2  |-  ( ph  <->  ps )
21sbcbii 3216 1  |-  ( [. A  /  a ]. ph  <->  [. A  / 
a ]. ps )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    e. wcel 1725   _Vcvv 2956   [.wsbc 3161
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-sbc 3162
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