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Theorem sbceq2a 3002
Description: Equality theorem for class substitution. Class version of sbequ12r 1861. (Contributed by NM, 4-Jan-2017.)
Assertion
Ref Expression
sbceq2a  |-  ( A  =  x  ->  ( [. A  /  x ]. ph  <->  ph ) )

Proof of Theorem sbceq2a
StepHypRef Expression
1 sbceq1a 3001 . . 3  |-  ( x  =  A  ->  ( ph 
<-> 
[. A  /  x ]. ph ) )
21eqcoms 2286 . 2  |-  ( A  =  x  ->  ( ph 
<-> 
[. A  /  x ]. ph ) )
32bicomd 192 1  |-  ( A  =  x  ->  ( [. A  /  x ]. ph  <->  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    = wceq 1623   [.wsbc 2991
This theorem is referenced by:  tfindes  4653  indexa  26412  fdc  26455  fdc1  26456  tratrbVD  28637
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-11 1715  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-sbc 2992
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