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Theorem snopsuppss 7837
 Description: The support of a singleton containing an ordered pair is a subset of the singleton containing the first element of the ordered pair, i.e. it is empty or the singleton itself. (Contributed by AV, 19-Jul-2019.)
Assertion
Ref Expression
snopsuppss ({⟨𝑋, 𝑌⟩} supp 𝑍) ⊆ {𝑋}

Proof of Theorem snopsuppss
StepHypRef Expression
1 suppssdm 7835 . 2 ({⟨𝑋, 𝑌⟩} supp 𝑍) ⊆ dom {⟨𝑋, 𝑌⟩}
2 dmsnopss 6064 . 2 dom {⟨𝑋, 𝑌⟩} ⊆ {𝑋}
31, 2sstri 3974 1 ({⟨𝑋, 𝑌⟩} supp 𝑍) ⊆ {𝑋}
 Colors of variables: wff setvar class Syntax hints:   ⊆ wss 3934  {csn 4559  ⟨cop 4565  dom cdm 5548  (class class class)co 7148   supp csupp 7822 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1905  ax-6 1964  ax-7 2009  ax-8 2110  ax-9 2118  ax-10 2139  ax-11 2154  ax-12 2170  ax-ext 2791  ax-sep 5194  ax-nul 5201  ax-pow 5257  ax-pr 5320  ax-un 7453 This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3an 1084  df-tru 1534  df-ex 1775  df-nf 1779  df-sb 2064  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-id 5453  df-xp 5554  df-rel 5555  df-cnv 5556  df-co 5557  df-dm 5558  df-rn 5559  df-res 5560  df-ima 5561  df-iota 6307  df-fun 6350  df-fv 6356  df-ov 7151  df-oprab 7152  df-mpo 7153  df-supp 7823 This theorem is referenced by:  snopfsupp  8848
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