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Theorem inf00 8700
 Description: The infimum regarding an empty base set is always the empty set. (Contributed by AV, 4-Sep-2020.)
Assertion
Ref Expression
inf00 inf(𝐵, ∅, 𝑅) = ∅

Proof of Theorem inf00
StepHypRef Expression
1 df-inf 8637 . 2 inf(𝐵, ∅, 𝑅) = sup(𝐵, ∅, 𝑅)
2 sup00 8658 . 2 sup(𝐵, ∅, 𝑅) = ∅
31, 2eqtri 2802 1 inf(𝐵, ∅, 𝑅) = ∅
 Colors of variables: wff setvar class Syntax hints:   = wceq 1601  ∅c0 4141  ◡ccnv 5354  supcsup 8634  infcinf 8635 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2055  ax-9 2116  ax-10 2135  ax-11 2150  ax-12 2163  ax-13 2334  ax-ext 2754 This theorem depends on definitions:  df-bi 199  df-an 387  df-or 837  df-tru 1605  df-ex 1824  df-nf 1828  df-sb 2012  df-clab 2764  df-cleq 2770  df-clel 2774  df-nfc 2921  df-ral 3095  df-rex 3096  df-rab 3099  df-v 3400  df-dif 3795  df-in 3799  df-ss 3806  df-nul 4142  df-sn 4399  df-uni 4672  df-sup 8636  df-inf 8637 This theorem is referenced by: (None)
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