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Theorem sbcbiiiOLD 26970
Description: Fully inferenced rewriting under an explicit substitution. (Contributed by Stefan O'Rear, 11-Oct-2014.)
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 3059 1  |-  ( [. A  /  a ]. ph  <->  [. A  / 
a ]. ps )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    e. wcel 1696   _Vcvv 2801   [.wsbc 3004
This theorem is referenced by:  2rexfrabdioph  26980  3rexfrabdioph  26981  4rexfrabdioph  26982  6rexfrabdioph  26983  7rexfrabdioph  26984  rmydioph  27210  expdiophlem2  27218
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  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-sbc 3005
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