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

Metamath Proof Explorer

Theorem ineq2d

Description: Equality deduction for intersection of two classes. (Contributed by NM, 10-Apr-1994)

		Ref	Expression
	Hypothesis	ineq1d.1	$⊢ φ \to A = B$
	Assertion	ineq2d	$⊢ φ \to C \cap A = C \cap B$

Step	Hyp	Ref	Expression
1		ineq1d.1	$⊢ φ \to A = B$
2		ineq2	$⊢ A = B \to C \cap A = C \cap B$
3	1 2	syl	$⊢ φ \to C \cap A = C \cap B$