Theorem difeq1i

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

	Ref	Expression
Hypothesis	difeq1i.1	⊢ 𝐴 = 𝐵
Assertion	difeq1i	⊢ ( 𝐴 ∖ 𝐶 ) = ( 𝐵 ∖ 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		difeq1i.1	⊢ 𝐴 = 𝐵
2		difeq1	⊢ ( 𝐴 = 𝐵 → ( 𝐴 ∖ 𝐶 ) = ( 𝐵 ∖ 𝐶 ) )
3	1 2	ax-mp	⊢ ( 𝐴 ∖ 𝐶 ) = ( 𝐵 ∖ 𝐶 )