Theorem e3

Description: Meta-connective form of syl8 . (Contributed by Alan Sare, 15-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e3.1	$$⊢\left(\phi ,\psi ,\chi \to \theta \right)$$
	e3.2	$$⊢\theta \to \tau$$
Assertion	e3	$$⊢\left(\phi ,\psi ,\chi \to \tau \right)$$

Proof

Step	Hyp	Ref	Expression
1		e3.1	$$⊢\left(\phi ,\psi ,\chi \to \theta \right)$$
2		e3.2	$$⊢\theta \to \tau$$
3	2	a1i	$$⊢\theta \to \left(\theta \to \tau \right)$$
4	1 1 3	e33	$$⊢\left(\phi ,\psi ,\chi \to \tau \right)$$