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Metamath Proof Explorer

Theorem bj-exalbial

Description: Adding a second quantifier over the same variable is a transparent operation, ( E. A. case). (Contributed by BJ, 20-Oct-2019)

		Ref	Expression
	Assertion	bj-exalbial	$⊢ \exists x \forall x φ \leftrightarrow \forall x φ$

Step	Hyp	Ref	Expression
1		nfa1	$⊢ Ⅎ x \forall x φ$
2	1	19.9	$⊢ \exists x \forall x φ \leftrightarrow \forall x φ$