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Theorem ovssunirn 7184
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 7151 . 2 (𝑋𝐹𝑌) = (𝐹‘⟨𝑋, 𝑌⟩)
2 fvssunirn 6692 . 2 (𝐹‘⟨𝑋, 𝑌⟩) ⊆ ran 𝐹
31, 2eqsstri 3999 1 (𝑋𝐹𝑌) ⊆ ran 𝐹
Colors of variables: wff setvar class
Syntax hints:  wss 3934  cop 4565   cuni 4830  ran crn 5549  cfv 6348  (class class class)co 7148
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2153  ax-12 2169  ax-ext 2791  ax-sep 5194  ax-nul 5201  ax-pow 5257  ax-pr 5320
This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3an 1083  df-tru 1533  df-ex 1774  df-nf 1778  df-sb 2063  df-mo 2616  df-eu 2648  df-clab 2798  df-cleq 2812  df-clel 2891  df-nfc 2961  df-ne 3015  df-ral 3141  df-rex 3142  df-rab 3145  df-v 3495  df-sbc 3771  df-dif 3937  df-un 3939  df-in 3941  df-ss 3950  df-nul 4290  df-if 4466  df-sn 4560  df-pr 4562  df-op 4566  df-uni 4831  df-br 5058  df-opab 5120  df-cnv 5556  df-dm 5558  df-rn 5559  df-iota 6307  df-fv 6356  df-ov 7151
This theorem is referenced by:  prdsval  16720  prdsplusg  16723  prdsmulr  16724  prdsvsca  16725  prdshom  16732  wunfunc  17161  wunnat  17218  homarw  17298  catcoppccl  17360  catcfuccl  17361  catcxpccl  17449
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