Theorem com3rgbi

Description: The following User's Proof is a Virtual Deduction proof completed automatically by the tools program completeusersproof.cmd, which invokes Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. The completed Virtual Deduction Proof (not shown) was minimized. The minimized proof is shown. (Contributed by Alan Sare, 18-Mar-2012) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	com3rgbi	$$⊢\left(\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)\right)\leftrightarrow \left(\chi \to \left(\phi \to \left(\psi \to \theta \right)\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		pm2.04	$$⊢\left(\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)\right)\to \left(\psi \to \left(\phi \to \left(\chi \to \theta \right)\right)\right)$$
2	1	com24	$$⊢\left(\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)\right)\to \left(\chi \to \left(\phi \to \left(\psi \to \theta \right)\right)\right)$$
3		pm2.04	$$⊢\left(\chi \to \left(\phi \to \left(\psi \to \theta \right)\right)\right)\to \left(\phi \to \left(\chi \to \left(\psi \to \theta \right)\right)\right)$$
4	3	com34	$$⊢\left(\chi \to \left(\phi \to \left(\psi \to \theta \right)\right)\right)\to \left(\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)\right)$$
5	2 4	impbii	$$⊢\left(\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)\right)\leftrightarrow \left(\chi \to \left(\phi \to \left(\psi \to \theta \right)\right)\right)$$