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	⊢ ( 𝜑 → ¬ 𝜓 )
	2falsed.2	⊢ ( 𝜑 → ¬ 𝜒 )
Assertion	2falsedOLD	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		2falsed.1	⊢ ( 𝜑 → ¬ 𝜓 )
2		2falsed.2	⊢ ( 𝜑 → ¬ 𝜒 )
3	1	pm2.21d	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
4	2	pm2.21d	⊢ ( 𝜑 → ( 𝜒 → 𝜓 ) )
5	3 4	impbid	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )