Theorem tbw-ax1

Description: The first of four axioms in the Tarski-Bernays-Wajsberg system. (Contributed by Anthony Hart, 13-Aug-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	tbw-ax1	$$⊢\left(\phi \to \psi \right)\to \left(\left(\psi \to \chi \right)\to \left(\phi \to \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		imim1	$$⊢\left(\phi \to \psi \right)\to \left(\left(\psi \to \chi \right)\to \left(\phi \to \chi \right)\right)$$