Theorem 0ima

Description: Image under the empty relation. (Contributed by FL, 11-Jan-2007)

	Ref	Expression
Assertion	0ima	⊢ ( ∅ “ 𝐴 ) = ∅

Proof

Step	Hyp	Ref	Expression
1		imassrn	⊢ ( ∅ “ 𝐴 ) ⊆ ran ∅
2		rn0	⊢ ran ∅ = ∅
3	1 2	sseqtri	⊢ ( ∅ “ 𝐴 ) ⊆ ∅
4		0ss	⊢ ∅ ⊆ ( ∅ “ 𝐴 )
5	3 4	eqssi	⊢ ( ∅ “ 𝐴 ) = ∅