Theorem tb-ax3

Description: The third of three axioms in the Tarski-Bernays axiom system.

This axiom, along with ax-mp , tb-ax1 , and tb-ax2 , can be used to derive any theorem or rule that uses only -> . (Contributed by Anthony Hart, 16-Aug-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	tb-ax3	$$⊢\left(\left(\phi \to \psi \right)\to \phi \right)\to \phi$$

Proof

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