Theorem imaeq1i

Description: Equality theorem for image. (Contributed by NM, 21-Dec-2008)

	Ref	Expression
Hypothesis	imaeq1i.1	⊢ 𝐴 = 𝐵
Assertion	imaeq1i	⊢ ( 𝐴 “ 𝐶 ) = ( 𝐵 “ 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		imaeq1i.1	⊢ 𝐴 = 𝐵
2		imaeq1	⊢ ( 𝐴 = 𝐵 → ( 𝐴 “ 𝐶 ) = ( 𝐵 “ 𝐶 ) )
3	1 2	ax-mp	⊢ ( 𝐴 “ 𝐶 ) = ( 𝐵 “ 𝐶 )