Theorem tb-ax3 34553

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

This axiom, along with ax-mp 5, tb-ax1 34551, and tb-ax2 34552, 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.)

Assertion

Ref	Expression
tb-ax3	⊢ (((𝜑 → 𝜓) → 𝜑) → 𝜑)

Proof of Theorem tb-ax3

Step	Hyp	Ref	Expression
1		peirce 201	1 ⊢ (((𝜑 → 𝜓) → 𝜑) → 𝜑)

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by:  re1ax2lem  34555  re1ax2  34556