Theorem hashsnlei

Description: Get an upper bound on a concretely specified finite set. Base case: singleton set. (Contributed by Mario Carneiro, 11-Feb-2015) (Proof shortened by AV, 23-Feb-2021)

	Ref	Expression
Assertion	hashsnlei	$$⊢\left(\left\{A\right\}\in \mathrm{Fin}\wedge \left|\left\{A\right\}\right|\le 1\right)$$

Proof

Step	Hyp	Ref	Expression
1		snfi	$$⊢\left\{A\right\}\in \mathrm{Fin}$$
2		hashsnle1	$$⊢\left|\left\{A\right\}\right|\le 1$$
3	1 2	pm3.2i	$$⊢\left(\left\{A\right\}\in \mathrm{Fin}\wedge \left|\left\{A\right\}\right|\le 1\right)$$