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Theorem reldmdsmm 19373
 Description: The direct sum is a well-behaved binary operator. (Contributed by Stefan O'Rear, 7-Jan-2015.)
Assertion
Ref Expression
reldmdsmm m

Proof of Theorem reldmdsmm
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-dsmm 19372 . 2 m ss
21reldmmpt2 6426 1 m
 Colors of variables: wff setvar class Syntax hints:   wcel 1904   wne 2641  crab 2760  cvv 3031   cdm 4839   wrel 4844  cfv 5589  (class class class)co 6308  cixp 7540  cfn 7587  cbs 15199   ↾s cress 15200  c0g 15416  scprds 15422   m cdsmm 19371 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-eu 2323  df-mo 2324  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-br 4396  df-opab 4455  df-xp 4845  df-rel 4846  df-dm 4849  df-oprab 6312  df-mpt2 6313  df-dsmm 19372 This theorem is referenced by:  dsmmval  19374  dsmmval2  19376
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