Theorem ifporcor

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

	Ref	Expression
Assertion	ifporcor	$$⊢if-\left(\phi ,\phi ,\psi \right)\leftrightarrow if-\left(\psi ,\psi ,\phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		orcom	$$⊢\left(\phi \vee \psi \right)\leftrightarrow \left(\psi \vee \phi \right)$$
2		ifpdfor2	$$⊢\left(\phi \vee \psi \right)\leftrightarrow if-\left(\phi ,\phi ,\psi \right)$$
3		ifpdfor2	$$⊢\left(\psi \vee \phi \right)\leftrightarrow if-\left(\psi ,\psi ,\phi \right)$$
4	1 2 3	3bitr3i	$$⊢if-\left(\phi ,\phi ,\psi \right)\leftrightarrow if-\left(\psi ,\psi ,\phi \right)$$