The objective was to determine the effect of using core animals from different generations in single-step genomic BLUP with the Algorithm for Proven and Young (APY). Effective population size and number of independent chromosome segments (ICS) are limited in livestock populations indicating limited dimensionality of genomic information. The APY takes advantage of this dimensionality and assumes that breeding vales (BV) for noncore animals are functions of the BV for core animals. The core animals represent the same information as the ICS. Simulations comprised a moderately heritable trait for 95,010 animals and 50,000 genotypes for animals across 5 generations. Genotypes consisted of 25,500 SNP distributed across 15 chromosomes. Core animals were defined based on individual generations, equal representation across generations, and at random. For a sufficiently large core size, core definitions had the same accuracies (r² = 0.90 ± 0.01) and biases (β₁ = 1.02 ± 0.01) for young animals, even if the core animals had imperfect genotypes because of imputation. Using the youngest generations as core caused an increase in the number of rounds to convergence indicating some numerical instability with these core definitions. When 80% of genotyped animals had unknown parents, accuracy and bias were significantly better (P ≤ 0.05) for random and across-generation core definitions (r² = 0.71 ± 0.01; β = 0.75 ± 0.01) than for single generation core definitions (r² = 0.61 ± 0.01; β = 0.53 ± 0.01). This difference could result from improved relationship estimates between animals in different generations, because all generations were represented in the core partition that was directly inverted in APY. Thus, any subset of genotyped animals can be used to approximate the ICS when pedigrees are complete, but core animals should represent all generations when pedigrees are incomplete.