MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  tbw-ax3 Structured version   Visualization version   GIF version

Theorem tbw-ax3 1625
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 (((𝜑𝜓) → 𝜑) → 𝜑)

Proof of Theorem tbw-ax3
StepHypRef Expression
1 peirce 193 1 (((𝜑𝜓) → 𝜑) → 𝜑)
Colors of variables: wff setvar class
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  1628  tbwlem3  1630  re1luk2  1634
  Copyright terms: Public domain W3C validator