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Theorem inf00 6928
 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 6882 . 2 inf(𝐵, ∅, 𝑅) = sup(𝐵, ∅, 𝑅)
2 sup00 6900 . 2 sup(𝐵, ∅, 𝑅) = ∅
31, 2eqtri 2161 1 inf(𝐵, ∅, 𝑅) = ∅
 Colors of variables: wff set class Syntax hints:   = wceq 1332  ∅c0 3369  ◡ccnv 4547  supcsup 6879  infcinf 6880 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-fal 1338  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-rex 2423  df-rab 2426  df-v 2692  df-dif 3079  df-in 3083  df-ss 3090  df-nul 3370  df-sn 3539  df-uni 3746  df-sup 6881  df-inf 6882 This theorem is referenced by: (None)
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