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Metamath Proof Explorer

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	⊢ ( { 𝐴 } ∈ Fin ∧ ( ♯ ‘ { 𝐴 } ) ≤ 1 )

Proof

Step	Hyp	Ref	Expression
1		snfi	⊢ { 𝐴 } ∈ Fin
2		hashsnle1	⊢ ( ♯ ‘ { 𝐴 } ) ≤ 1
3	1 2	pm3.2i	⊢ ( { 𝐴 } ∈ Fin ∧ ( ♯ ‘ { 𝐴 } ) ≤ 1 )