Theorem imaeq1d

Description: Equality theorem for image. (Contributed by FL, 15-Dec-2006)

	Ref	Expression
Hypothesis	imaeq1d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	imaeq1d	⊢ ( 𝜑 → ( 𝐴 “ 𝐶 ) = ( 𝐵 “ 𝐶 ) )

Proof

Step	Hyp	Ref	Expression
1		imaeq1d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		imaeq1	⊢ ( 𝐴 = 𝐵 → ( 𝐴 “ 𝐶 ) = ( 𝐵 “ 𝐶 ) )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐴 “ 𝐶 ) = ( 𝐵 “ 𝐶 ) )