Theorem ee11an

Description: e11an without virtual deductions. syl22anc is also e11an without virtual deductions, exept with a different order of hypotheses. (Contributed by Alan Sare, 8-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee11an.1	$$⊢\phi \to \psi$$
	ee11an.2	$$⊢\phi \to \chi$$
	ee11an.3	$$⊢\left(\psi \wedge \chi \right)\to \theta$$
Assertion	ee11an	$$⊢\phi \to \theta$$

Proof

Step	Hyp	Ref	Expression
1		ee11an.1	$$⊢\phi \to \psi$$
2		ee11an.2	$$⊢\phi \to \chi$$
3		ee11an.3	$$⊢\left(\psi \wedge \chi \right)\to \theta$$
4	3	ex	$$⊢\psi \to \left(\chi \to \theta \right)$$
5	1 2 4	sylc	$$⊢\phi \to \theta$$