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Metamath Proof Explorer

Theorem difeq2i

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

Ref Expression
Hypothesis difeq1i.1 ⊢ 𝐴 = 𝐵
Assertion difeq2i ( 𝐶 ∖ 𝐴 ) = ( 𝐶 ∖ 𝐵 )

Proof

Step Hyp Ref Expression
1 difeq1i.1 ⊢ 𝐴 = 𝐵
2 difeq2 ⊢ ( 𝐴 = 𝐵 → ( 𝐶 ∖ 𝐴 ) = ( 𝐶 ∖ 𝐵 ) )
3 1 2 ax-mp ⊢ ( 𝐶 ∖ 𝐴 ) = ( 𝐶 ∖ 𝐵 )