Theorem imaeq1d

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

	Ref	Expression
Hypothesis	imaeq1d.1	$$⊢\phi \to A=B$$
Assertion	imaeq1d	$$⊢\phi \to A\left[C\right]=B\left[C\right]$$

Proof

Step	Hyp	Ref	Expression
1		imaeq1d.1	$$⊢\phi \to A=B$$
2		imaeq1	$$⊢A=B\to A\left[C\right]=B\left[C\right]$$
3	1 2	syl	$$⊢\phi \to A\left[C\right]=B\left[C\right]$$