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Theorem ovssunirn 6107
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 6084 . 2  |-  ( X F Y )  =  ( F `  <. X ,  Y >. )
2 fvssunirn 5754 . 2  |-  ( F `
 <. X ,  Y >. )  C_  U. ran  F
31, 2eqsstri 3378 1  |-  ( X F Y )  C_  U.
ran  F
Colors of variables: wff set class
Syntax hints:    C_ wss 3320   <.cop 3817   U.cuni 4015   ran crn 4879   ` cfv 5454  (class class class)co 6081
This theorem is referenced by:  prdsval  13678  prdsplusg  13681  prdsmulr  13682  prdsvsca  13683  prdshom  13689  wunfunc  14096  wunnat  14153  homarw  14201  catcoppccl  14263  catcfuccl  14264  catcxpccl  14304
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-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pow 4377  ax-pr 4403
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-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-sbc 3162  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-opab 4267  df-cnv 4886  df-dm 4888  df-rn 4889  df-iota 5418  df-fv 5462  df-ov 6084
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