This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem ineq2i

Description: Equality inference for intersection of two classes. (Contributed by NM, 26-Dec-1993)

Ref Expression
Hypothesis ineq1i.1 ⊢ A = B
Assertion ineq2i ⊢ C ∩ A = C ∩ B

Proof

Step Hyp Ref Expression
1 ineq1i.1 ⊢ A = B
2 ineq2 ⊢ A = B → C ∩ A = C ∩ B
3 1 2 ax-mp ⊢ C ∩ A = C ∩ B