Theorem ifpdfor2

Description: Define or in terms of conditional logic operator. (Contributed by RP, 20-Apr-2020)

	Ref	Expression
Assertion	ifpdfor2	$$⊢\left(\phi \vee \psi \right)\leftrightarrow if-\left(\phi ,\phi ,\psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		pm2.1	$$⊢\left(\neg \phi \vee \phi \right)$$
2	1	biantrur	$$⊢\left(\phi \vee \psi \right)\leftrightarrow \left(\left(\neg \phi \vee \phi \right)\wedge \left(\phi \vee \psi \right)\right)$$
3		dfifp4	$$⊢if-\left(\phi ,\phi ,\psi \right)\leftrightarrow \left(\left(\neg \phi \vee \phi \right)\wedge \left(\phi \vee \psi \right)\right)$$
4	2 3	bitr4i	$$⊢\left(\phi \vee \psi \right)\leftrightarrow if-\left(\phi ,\phi ,\psi \right)$$