Theorem ifporcor

Description: Corollary of commutation of or. (Contributed by RP, 20-Apr-2020)

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

Proof

Step	Hyp	Ref	Expression
1		orcom	⊢ ( ( 𝜑 ∨ 𝜓 ) ↔ ( 𝜓 ∨ 𝜑 ) )
2		ifpdfor2	⊢ ( ( 𝜑 ∨ 𝜓 ) ↔ if- ( 𝜑 , 𝜑 , 𝜓 ) )
3		ifpdfor2	⊢ ( ( 𝜓 ∨ 𝜑 ) ↔ if- ( 𝜓 , 𝜓 , 𝜑 ) )
4	1 2 3	3bitr3i	⊢ ( if- ( 𝜑 , 𝜑 , 𝜓 ) ↔ if- ( 𝜓 , 𝜓 , 𝜑 ) )