While Trump didn't offer any numbers to support this claim, a Defense Department-commissioned study published last year by the Rand Corp. provides exhaustive estimates of transgender servicemembers' potential medical costs.

Considering the prevalence of transgender servicemembers among the active duty military and the typical health-care costs for gender-transition-related medical treatment, the Rand study estimated that these treatments would cost the military between $2.4 million and $8.4 million annually.

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The study didn't include estimates of these costs for reservists, because of their “highly limited military health care eligibility.” It also didn't include estimates for retirees or military family members, because many of those individuals may also have “limited eligibility” for care via military treatment facilities.

“The implication is that even in the most extreme scenario that we were able to identify … we expect only a 0.13-percent ($8.4 million out of $6.2 billion) increase in health care spending,” Rand's authors concluded.

By contrast, total military spending on erectile dysfunction medicines amounts to $84 million annually, according to an analysis by the Military Times — 10 times the cost of annual transition-related medical care for active duty transgender servicemembers.

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The military spends $41.6 million annually on Viagra alone, according to the Military Times analysis — roughly five times the estimated spending on transition-related medical care for transgender troops.

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The cost of providing medical care to transgender servicemembers, in other words, is negligible, and hardly “tremendous,” as the president put it.