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Theorem sbcid 3179
Description: An identity theorem for substitution. See sbid 1948. (Contributed by Mario Carneiro, 18-Feb-2017.)
Assertion
Ref Expression
sbcid  |-  ( [. x  /  x ]. ph  <->  ph )

Proof of Theorem sbcid
StepHypRef Expression
1 sbsbc 3167 . 2  |-  ( [ x  /  x ] ph 
<-> 
[. x  /  x ]. ph )
2 sbid 1948 . 2  |-  ( [ x  /  x ] ph 
<-> 
ph )
31, 2bitr3i 244 1  |-  ( [. x  /  x ]. ph  <->  ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 178   [wsb 1659   [.wsbc 3163
This theorem is referenced by:  csbid  3260  snfil  17898  filuni  17919  ex-natded9.26  21729  bnj605  29340
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-11 1762  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-sbc 3164
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