Theorem eximdh

Description: Deduction from Theorem 19.22 of Margaris p. 90. (Contributed by NM, 20-May-1996)

	Ref	Expression
Hypotheses	eximdh.1	$$⊢\phi \to \forall x\phi$$
	eximdh.2	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	eximdh	$$⊢\phi \to \left(\exists x\psi \to \exists x\chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		eximdh.1	$$⊢\phi \to \forall x\phi$$
2		eximdh.2	$$⊢\phi \to \left(\psi \to \chi \right)$$
3	2	aleximi	$$⊢\forall x\phi \to \left(\exists x\psi \to \exists x\chi \right)$$
4	1 3	syl	$$⊢\phi \to \left(\exists x\psi \to \exists x\chi \right)$$