Theorem 2falsedOLD

Description: Obsolete version of 2falsed as of 11-Apr-2024. (Contributed by NM, 11-Oct-2013) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	2falsed.1	$$⊢\phi \to \neg \psi$$
	2falsed.2	$$⊢\phi \to \neg \chi$$
Assertion	2falsedOLD	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		2falsed.1	$$⊢\phi \to \neg \psi$$
2		2falsed.2	$$⊢\phi \to \neg \chi$$
3	1	pm2.21d	$$⊢\phi \to \left(\psi \to \chi \right)$$
4	2	pm2.21d	$$⊢\phi \to \left(\chi \to \psi \right)$$
5	3 4	impbid	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$