Theorem ima0

Description: Image of the empty set. Theorem 3.16(ii) of Monk1 p. 38. (Contributed by NM, 20-May-1998)

	Ref	Expression
Assertion	ima0	⊢ ( 𝐴 “ ∅ ) = ∅

Proof

Step	Hyp	Ref	Expression
1		df-ima	⊢ ( 𝐴 “ ∅ ) = ran ( 𝐴 ↾ ∅ )
2		res0	⊢ ( 𝐴 ↾ ∅ ) = ∅
3	2	rneqi	⊢ ran ( 𝐴 ↾ ∅ ) = ran ∅
4		rn0	⊢ ran ∅ = ∅
5	1 3 4	3eqtri	⊢ ( 𝐴 “ ∅ ) = ∅