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Metamath Proof Explorer

Theorem r19.29an

Description: A commonly used pattern in the spirit of r19.29 . (Contributed by Thierry Arnoux, 29-Dec-2019) (Proof shortened by Wolf Lammen, 17-Jun-2023)

		Ref	Expression
	Hypothesis	rexlimdva2.1	$⊢ ((φ \land x \in A) \land ψ) \to χ$
	Assertion	r19.29an	$⊢ (φ \land \exists x \in A ψ) \to χ$

Proof

Step	Hyp	Ref	Expression
1		rexlimdva2.1	$⊢ ((φ \land x \in A) \land ψ) \to χ$
2	1	rexlimdva2	$⊢ φ \to (\exists x \in A ψ \to χ)$
3	2	imp	$⊢ (φ \land \exists x \in A ψ) \to χ$