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Theorem sbcbiiiOLD 26867
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 3046 1  |-  ( [. A  /  a ]. ph  <->  [. A  / 
a ]. ps )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    e. wcel 1684   _Vcvv 2788   [.wsbc 2991
This theorem is referenced by:  2rexfrabdioph  26877  3rexfrabdioph  26878  4rexfrabdioph  26879  6rexfrabdioph  26880  7rexfrabdioph  26881  rmydioph  27107  expdiophlem2  27115
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-sbc 2992
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