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Theorem sbcid 3007
Description: An identity theorem for substitution. See sbid 1863. (Contributed by Mario Carneiro, 18-Feb-2017.)
Assertion
Ref Expression
sbcid  |-  ( [. x  /  x ]. ph  <->  ph )

Proof of Theorem sbcid
StepHypRef Expression
1 sbsbc 2995 . 2  |-  ( [ x  /  x ] ph 
<-> 
[. x  /  x ]. ph )
2 sbid 1863 . 2  |-  ( [ x  /  x ] ph 
<-> 
ph )
31, 2bitr3i 242 1  |-  ( [. x  /  x ]. ph  <->  ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 176   [wsb 1629   [.wsbc 2991
This theorem is referenced by:  ex-natded9.26  20806
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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