Theorem eceq1d

Description: Equality theorem for equivalence class (deduction form). (Contributed by Jim Kingdon, 31-Dec-2019)

	Ref	Expression
Hypothesis	eceq1d.1	$$⊢\phi \to A=B$$
Assertion	eceq1d	$$⊢\phi \to \left[A\right]C=\left[B\right]C$$

Proof

Step	Hyp	Ref	Expression
1		eceq1d.1	$$⊢\phi \to A=B$$
2		eceq1	$$⊢A=B\to \left[A\right]C=\left[B\right]C$$
3	1 2	syl	$$⊢\phi \to \left[A\right]C=\left[B\right]C$$