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Theorem ovssunirn 5900
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 5877 . 2  |-  ( X F Y )  =  ( F `  <. X ,  Y >. )
2 fvssunirn 5567 . 2  |-  ( F `
 <. X ,  Y >. )  C_  U. ran  F
31, 2eqsstri 3221 1  |-  ( X F Y )  C_  U.
ran  F
Colors of variables: wff set class
Syntax hints:    C_ wss 3165   <.cop 3656   U.cuni 3843   ran crn 4706   ` cfv 5271  (class class class)co 5874
This theorem is referenced by:  wunfunc  13789  wunnat  13846  homarw  13894  catcoppccl  13956  catcfuccl  13957  catcxpccl  13997
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-13 1698  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pow 4204  ax-pr 4230
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-sbc 3005  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-br 4040  df-opab 4094  df-cnv 4713  df-dm 4715  df-rn 4716  df-iota 5235  df-fv 5279  df-ov 5877
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