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Theorem ovssunirn 7193
 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 (𝑋𝐹𝑌) ⊆ ran 𝐹

Proof of Theorem ovssunirn
StepHypRef Expression
1 df-ov 7160 . 2 (𝑋𝐹𝑌) = (𝐹‘⟨𝑋, 𝑌⟩)
2 fvssunirn 6693 . 2 (𝐹‘⟨𝑋, 𝑌⟩) ⊆ ran 𝐹
31, 2eqsstri 3929 1 (𝑋𝐹𝑌) ⊆ ran 𝐹
 Colors of variables: wff setvar class Syntax hints:   ⊆ wss 3861  ⟨cop 4532  ∪ cuni 4802  ran crn 5530  ‘cfv 6341  (class class class)co 7157 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2114  ax-9 2122  ax-10 2143  ax-11 2159  ax-12 2176  ax-ext 2730  ax-sep 5174  ax-nul 5181  ax-pr 5303 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1087  df-tru 1542  df-fal 1552  df-ex 1783  df-nf 1787  df-sb 2071  df-mo 2558  df-eu 2589  df-clab 2737  df-cleq 2751  df-clel 2831  df-ne 2953  df-ral 3076  df-rex 3077  df-v 3412  df-sbc 3700  df-dif 3864  df-un 3866  df-in 3868  df-ss 3878  df-nul 4229  df-if 4425  df-sn 4527  df-pr 4529  df-op 4533  df-uni 4803  df-br 5038  df-opab 5100  df-cnv 5537  df-dm 5539  df-rn 5540  df-iota 6300  df-fv 6349  df-ov 7160 This theorem is referenced by:  prdsval  16801  prdsplusg  16804  prdsmulr  16805  prdsvsca  16806  prdshom  16813  wunfunc  17243  wunnat  17300  homarw  17387  catcoppccl  17449  catcfuccl  17450  catcxpccl  17538
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