Theorem ifpancor

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

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

Proof

Step	Hyp	Ref	Expression
1		ancom	$$⊢\left(\phi \wedge \psi \right)\leftrightarrow \left(\psi \wedge \phi \right)$$
2		ifpdfan2	$$⊢\left(\phi \wedge \psi \right)\leftrightarrow if-\left(\phi ,\psi ,\phi \right)$$
3		ifpdfan2	$$⊢\left(\psi \wedge \phi \right)\leftrightarrow if-\left(\psi ,\phi ,\psi \right)$$
4	1 2 3	3bitr3i	$$⊢if-\left(\phi ,\psi ,\phi \right)\leftrightarrow if-\left(\psi ,\phi ,\psi \right)$$