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Theorem ovssunirn 6321
Description: The result of an operation value is always a subset of the union of the range. (Contributed by Mario Carneiro, 12-Jan-2017.)
Assertion
Ref Expression
ovssunirn  |-  ( X F Y )  C_  U.
ran  F

Proof of Theorem ovssunirn
StepHypRef Expression
1 df-ov 6298 . 2  |-  ( X F Y )  =  ( F `  <. X ,  Y >. )
2 fvssunirn 5895 . 2  |-  ( F `
 <. X ,  Y >. )  C_  U. ran  F
31, 2eqsstri 3539 1  |-  ( X F Y )  C_  U.
ran  F
Colors of variables: wff setvar class
Syntax hints:    C_ wss 3481   <.cop 4039   U.cuni 4251   ran crn 5006   ` cfv 5594  (class class class)co 6295
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-8 1769  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4574  ax-nul 4582  ax-pow 4631  ax-pr 4692
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-mo 2280  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2822  df-rex 2823  df-rab 2826  df-v 3120  df-sbc 3337  df-dif 3484  df-un 3486  df-in 3488  df-ss 3495  df-nul 3791  df-if 3946  df-sn 4034  df-pr 4036  df-op 4040  df-uni 4252  df-br 4454  df-opab 4512  df-cnv 5013  df-dm 5015  df-rn 5016  df-iota 5557  df-fv 5602  df-ov 6298
This theorem is referenced by:  prdsval  14727  prdsplusg  14730  prdsmulr  14731  prdsvsca  14732  prdshom  14739  wunfunc  15143  wunnat  15200  homarw  15248  catcoppccl  15310  catcfuccl  15311  catcxpccl  15351
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