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Metamath Proof Explorer

Theorem ineq1d

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

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

Step	Hyp	Ref	Expression
1		ineq1d.1	$⊢ φ \to A = B$
2		ineq1	$⊢ A = B \to A \cap C = B \cap C$
3	1 2	syl	$⊢ φ \to A \cap C = B \cap C$