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Theorem tendoplcbv 34413
 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 5878 . . . . 5
32coeq1d 5001 . . . 4
43mpteq2dv 4483 . . 3
5 fveq1 5878 . . . . . 6
65coeq2d 5002 . . . . 5
76mpteq2dv 4483 . . . 4
8 fveq2 5879 . . . . . 6
9 fveq2 5879 . . . . . 6
108, 9coeq12d 5004 . . . . 5
1110cbvmptv 4488 . . . 4
127, 11syl6eq 2521 . . 3
134, 12cbvmpt2v 6390 . 2
141, 13eqtri 2493 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1452   cmpt 4454   ccom 4843  cfv 5589   cmpt2 6310 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-sep 4518  ax-nul 4527  ax-pr 4639 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-rex 2762  df-rab 2765  df-v 3033  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-sn 3960  df-pr 3962  df-op 3966  df-uni 4191  df-br 4396  df-opab 4455  df-mpt 4456  df-co 4848  df-iota 5553  df-fv 5597  df-oprab 6312  df-mpt2 6313 This theorem is referenced by:  tendopl  34414
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