Theorem tbw-ax3 1708

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

Assertion

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

Proof of Theorem tbw-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:  tbwlem1  1711  tbwlem3  1713  re1luk2  1717