Theorem unitreslOLD

Description: Obsolete version of olcnd as of 13-Apr-2024. (Contributed by Giovanni Mascellani, 15-Sep-2017) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	olcnd.1	$$⊢\phi \to \left(\psi \vee \chi \right)$$
	olcnd.2	$$⊢\phi \to \neg \chi$$
Assertion	unitreslOLD	$$⊢\phi \to \psi$$

Proof

Step	Hyp	Ref	Expression
1		olcnd.1	$$⊢\phi \to \left(\psi \vee \chi \right)$$
2		olcnd.2	$$⊢\phi \to \neg \chi$$
3		orcom	$$⊢\left(\psi \vee \chi \right)\leftrightarrow \left(\chi \vee \psi \right)$$
4		df-or	$$⊢\left(\chi \vee \psi \right)\leftrightarrow \left(\neg \chi \to \psi \right)$$
5	3 4	sylbb	$$⊢\left(\psi \vee \chi \right)\to \left(\neg \chi \to \psi \right)$$
6	1 2 5	sylc	$$⊢\phi \to \psi$$