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Theorem sbcid 2839
Description: An identity theorem for substitution. See sbid 1699. (Contributed by Mario Carneiro, 18-Feb-2017.)
Assertion
Ref Expression
sbcid  |-  ( [. x  /  x ]. ph  <->  ph )

Proof of Theorem sbcid
StepHypRef Expression
1 sbsbc 2828 . 2  |-  ( [ x  /  x ] ph 
<-> 
[. x  /  x ]. ph )
2 sbid 1699 . 2  |-  ( [ x  /  x ] ph 
<-> 
ph )
31, 2bitr3i 184 1  |-  ( [. x  /  x ]. ph  <->  ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 103   [wsb 1687   [.wsbc 2824
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-sbc 2825
This theorem is referenced by:  csbid  2924
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