Metamath Proof Explorer


Theorem ineq1i

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

Ref Expression
Hypothesis ineq1i.1 A = B
Assertion ineq1i A C = B C

Proof

Step Hyp Ref Expression
1 ineq1i.1 A = B
2 ineq1 A = B A C = B C
3 1 2 ax-mp A C = B C