holdsIfAndOnlyIf
P90305
predicate
Indicates that a condition or relationship is true exactly when, and only when, another specified condition holds, establishing a bidirectional logical equivalence between them.
All labels observed (2)
| Label | Occurrences |
|---|---|
| isZeroIfAndOnlyIf | 2 |
| holdsIfAndOnlyIf canonical | 1 |
Description generation (PDg)
The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.
Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning. # Instructions Focus on describing the relationship, not the entities themselves. # Response Format Begin the description with \' Indicates...\'
Input
Predicate: holdsIfAndOnlyIf
Generated description
Indicates that a condition or relationship is true exactly when, and only when, another specified condition holds, establishing a bidirectional logical equivalence between them.
Sample triples (3)
| Subject | Object |
|---|---|
| Cauchy convergence criterion | every Cauchy sequence converges in a complete metric space ⓘ |
| Weyl tensor | spacetime is locally conformally flat (dimension ≥ 4) via predicate surface "isZeroIfAndOnlyIf" ⓘ |
| distance covariance | random variables are independent via predicate surface "isZeroIfAndOnlyIf" ⓘ |