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Theorem ovssunirn 6299
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 6273 . 2  |-  ( X F Y )  =  ( F `  <. X ,  Y >. )
2 fvssunirn 5871 . 2  |-  ( F `
 <. X ,  Y >. )  C_  U. ran  F
31, 2eqsstri 3519 1  |-  ( X F Y )  C_  U.
ran  F
Colors of variables: wff setvar class
Syntax hints:    C_ wss 3461   <.cop 4022   U.cuni 4235   ran crn 4989   ` cfv 5570  (class class class)co 6270
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-8 1825  ax-9 1827  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004  ax-ext 2432  ax-sep 4560  ax-nul 4568  ax-pow 4615  ax-pr 4676
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 973  df-tru 1401  df-ex 1618  df-nf 1622  df-sb 1745  df-eu 2288  df-mo 2289  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2651  df-ral 2809  df-rex 2810  df-rab 2813  df-v 3108  df-sbc 3325  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3784  df-if 3930  df-sn 4017  df-pr 4019  df-op 4023  df-uni 4236  df-br 4440  df-opab 4498  df-cnv 4996  df-dm 4998  df-rn 4999  df-iota 5534  df-fv 5578  df-ov 6273
This theorem is referenced by:  prdsval  14947  prdsplusg  14950  prdsmulr  14951  prdsvsca  14952  prdshom  14959  wunfunc  15390  wunnat  15447  homarw  15527  catcoppccl  15589  catcfuccl  15590  catcxpccl  15678
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