Theorem csbeq1d

Description: Equality deduction for proper substitution into a class. (Contributed by NM, 3-Dec-2005)

	Ref	Expression
Hypothesis	csbeq1d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	csbeq1d	⊢ ( 𝜑 → ⦋ 𝐴 / 𝑥 ⦌ 𝐶 = ⦋ 𝐵 / 𝑥 ⦌ 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		csbeq1d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		csbeq1	⊢ ( 𝐴 = 𝐵 → ⦋ 𝐴 / 𝑥 ⦌ 𝐶 = ⦋ 𝐵 / 𝑥 ⦌ 𝐶 )
3	1 2	syl	⊢ ( 𝜑 → ⦋ 𝐴 / 𝑥 ⦌ 𝐶 = ⦋ 𝐵 / 𝑥 ⦌ 𝐶 )