Theorem eexinst01

Description: exinst01 without virtual deductions. (Contributed by Alan Sare, 21-Apr-2013) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	eexinst01.1	$$⊢\exists x\psi$$
	eexinst01.2	$$⊢\phi \to \left(\psi \to \chi \right)$$
	eexinst01.3	$$⊢\phi \to \forall x\phi$$
	eexinst01.4	$$⊢\chi \to \forall x\chi$$
Assertion	eexinst01	$$⊢\phi \to \chi$$

Proof

Step	Hyp	Ref	Expression
1		eexinst01.1	$$⊢\exists x\psi$$
2		eexinst01.2	$$⊢\phi \to \left(\psi \to \chi \right)$$
3		eexinst01.3	$$⊢\phi \to \forall x\phi$$
4		eexinst01.4	$$⊢\chi \to \forall x\chi$$
5	3 4 2	exlimdh	$$⊢\phi \to \left(\exists x\psi \to \chi \right)$$
6	1 5	mpi	$$⊢\phi \to \chi$$