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

Metamath Proof Explorer

Theorem iineq1d

Description: Equality theorem for indexed intersection. (Contributed by Glauco Siliprandi, 8-Apr-2021)

		Ref	Expression
	Hypothesis	iineq1d.1	$⊢ φ \to A = B$
	Assertion	iineq1d	$⊢ φ \to ⋂_{x \in A} C = ⋂_{x \in B} C$

Step	Hyp	Ref	Expression
1		iineq1d.1	$⊢ φ \to A = B$
2		iineq1	$⊢ A = B \to ⋂_{x \in A} C = ⋂_{x \in B} C$
3	1 2	syl	$⊢ φ \to ⋂_{x \in A} C = ⋂_{x \in B} C$