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Theorem tendoplcbv 31509
 Description: Define sum operation for trace-perserving endomorphisms. Change bound variables to isolate them later. (Contributed by NM, 11-Jun-2013.)
Hypothesis
Ref Expression
tendoplcbv.p
Assertion
Ref Expression
tendoplcbv
Distinct variable groups:   ,,,,   ,,,,,,
Allowed substitution hints:   (,,,,,)   (,)

Proof of Theorem tendoplcbv
StepHypRef Expression
1 tendoplcbv.p . 2
2 fveq1 5719 . . . . 5
32coeq1d 5026 . . . 4
43mpteq2dv 4288 . . 3
5 fveq1 5719 . . . . . 6
65coeq2d 5027 . . . . 5
76mpteq2dv 4288 . . . 4
8 fveq2 5720 . . . . . 6
9 fveq2 5720 . . . . . 6
108, 9coeq12d 5029 . . . . 5
1110cbvmptv 4292 . . . 4
127, 11syl6eq 2483 . . 3
134, 12cbvmpt2v 6144 . 2
141, 13eqtri 2455 1
 Colors of variables: wff set class Syntax hints:   wceq 1652   cmpt 4258   ccom 4874  cfv 5446   cmpt2 6075 This theorem is referenced by:  tendopl  31510 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-mpt 4260  df-co 4879  df-iota 5410  df-fv 5454  df-oprab 6077  df-mpt2 6078
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