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Definition df-inf 6921
 Description: Define the infimum of class . It is meaningful when is a relation that strictly orders and when the infimum exists. For example, could be 'less than', could be the set of real numbers, and could be the set of all positive reals; in this case the infimum is 0. The infimum is defined as the supremum using the converse ordering relation. In the given example, 0 is the supremum of all reals (greatest real number) for which all positive reals are greater. (Contributed by AV, 2-Sep-2020.)
Assertion
Ref Expression
df-inf inf

Detailed syntax breakdown of Definition df-inf
StepHypRef Expression
1 cA . . 3
2 cB . . 3
3 cR . . 3
41, 2, 3cinf 6919 . 2 inf
53ccnv 4582 . . 3
61, 2, 5csup 6918 . 2
74, 6wceq 1335 1 inf
 Colors of variables: wff set class This definition is referenced by:  infeq1  6947  infeq2  6950  infeq3  6951  infeq123d  6952  nfinf  6953  eqinfti  6956  infvalti  6958  infclti  6959  inflbti  6960  infglbti  6961  infsnti  6966  inf00  6967  infisoti  6968  dfinfre  8810  infrenegsupex  9488  infxrnegsupex  11142
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