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Metamath Proof Explorer

Theorem rmobidv

Description: Formula-building rule for restricted at-most-one quantifier (deduction form). (Contributed by NM, 16-Jun-2017)

		Ref	Expression
	Hypothesis	rmobidv.1	$⊢ φ \to (ψ \leftrightarrow χ)$
	Assertion	rmobidv	$⊢ φ \to (\exists^{} x \in A ψ \leftrightarrow \exists^{} x \in A χ)$

Step	Hyp	Ref	Expression
1		rmobidv.1	$⊢ φ \to (ψ \leftrightarrow χ)$
2	1	adantr	$⊢ (φ \land x \in A) \to (ψ \leftrightarrow χ)$
3	2	rmobidva	$⊢ φ \to (\exists^{} x \in A ψ \leftrightarrow \exists^{} x \in A χ)$