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Theorem tendo0cbv 30975
Description: Define additive identity for trace-perserving endomorphisms. Change bound variable to isolate it later. (Contributed by NM, 11-Jun-2013.)
Hypothesis
Ref Expression
tendo0cbv.o  |-  O  =  ( f  e.  T  |->  (  _I  |`  B ) )
Assertion
Ref Expression
tendo0cbv  |-  O  =  ( g  e.  T  |->  (  _I  |`  B ) )
Distinct variable groups:    B, f    B, g    T, f    T, g
Allowed substitution hints:    O( f, g)

Proof of Theorem tendo0cbv
StepHypRef Expression
1 tendo0cbv.o . 2  |-  O  =  ( f  e.  T  |->  (  _I  |`  B ) )
2 eqidd 2284 . . 3  |-  ( f  =  g  ->  (  _I  |`  B )  =  (  _I  |`  B ) )
32cbvmptv 4111 . 2  |-  ( f  e.  T  |->  (  _I  |`  B ) )  =  ( g  e.  T  |->  (  _I  |`  B ) )
41, 3eqtri 2303 1  |-  O  =  ( g  e.  T  |->  (  _I  |`  B ) )
Colors of variables: wff set class
Syntax hints:    = wceq 1623    e. cmpt 4077    _I cid 4304    |` cres 4691
This theorem is referenced by:  tendo02  30976  tendo0cl  30979
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-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-opab 4078  df-mpt 4079
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