This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem eexinst11

Description: exinst11 without virtual deductions. (Contributed by Alan Sare, 21-Apr-2013) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	eexinst11.1	$⊢ φ \to \exists x ψ$
	eexinst11.2	$⊢ φ \to (ψ \to χ)$
	eexinst11.3	$⊢ φ \to \forall x φ$
	eexinst11.4	$⊢ χ \to \forall x χ$
Assertion	eexinst11	$⊢ φ \to χ$

Proof

Step	Hyp	Ref	Expression
1		eexinst11.1	$⊢ φ \to \exists x ψ$
2		eexinst11.2	$⊢ φ \to (ψ \to χ)$
3		eexinst11.3	$⊢ φ \to \forall x φ$
4		eexinst11.4	$⊢ χ \to \forall x χ$
5	3 4 2	exlimdh	$⊢ φ \to (\exists x ψ \to χ)$
6	1 5	syl5com	$⊢ φ \to (φ \to χ)$
7	6	pm2.43i	$⊢ φ \to χ$