Theorem difeq1d

Description: Deduction adding difference to the right in a class equality. (Contributed by NM, 15-Nov-2002)

	Ref	Expression
Hypothesis	difeq1d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	difeq1d	⊢ ( 𝜑 → ( 𝐴 ∖ 𝐶 ) = ( 𝐵 ∖ 𝐶 ) )

Proof

Step	Hyp	Ref	Expression
1		difeq1d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		difeq1	⊢ ( 𝐴 = 𝐵 → ( 𝐴 ∖ 𝐶 ) = ( 𝐵 ∖ 𝐶 ) )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐴 ∖ 𝐶 ) = ( 𝐵 ∖ 𝐶 ) )