Theorem ifpnotnotb

Description: Factor conditional logic operator over negation in terms 2 and 3. (Contributed by RP, 21-Apr-2020)

	Ref	Expression
Assertion	ifpnotnotb	⊢ ( if- ( 𝜑 , ¬ 𝜓 , ¬ 𝜒 ) ↔ ¬ if- ( 𝜑 , 𝜓 , 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		ifpnot23	⊢ ( ¬ if- ( 𝜑 , 𝜓 , 𝜒 ) ↔ if- ( 𝜑 , ¬ 𝜓 , ¬ 𝜒 ) )
2	1	bicomi	⊢ ( if- ( 𝜑 , ¬ 𝜓 , ¬ 𝜒 ) ↔ ¬ if- ( 𝜑 , 𝜓 , 𝜒 ) )