Theorem ifpbicor

Description: Corollary of commutation of biconditional. (Contributed by RP, 25-Apr-2020)

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

Proof

Step	Hyp	Ref	Expression
1		bicom	⊢ ( ( 𝜑 ↔ 𝜓 ) ↔ ( 𝜓 ↔ 𝜑 ) )
2		ifpdfbi	⊢ ( ( 𝜑 ↔ 𝜓 ) ↔ if- ( 𝜑 , 𝜓 , ¬ 𝜓 ) )
3		ifpdfbi	⊢ ( ( 𝜓 ↔ 𝜑 ) ↔ if- ( 𝜓 , 𝜑 , ¬ 𝜑 ) )
4	1 2 3	3bitr3i	⊢ ( if- ( 𝜑 , 𝜓 , ¬ 𝜓 ) ↔ if- ( 𝜓 , 𝜑 , ¬ 𝜑 ) )