Users' Mathboxes Mathbox for Anthony Hart < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  tb-ax3 Structured version   Visualization version   GIF version

Theorem tb-ax3 31550
Description: The third of three axioms in the Tarski-Bernays axiom system.

This axiom, along with ax-mp 5, tb-ax1 31548, and tb-ax2 31549, 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
tb-ax3 (((𝜑𝜓) → 𝜑) → 𝜑)

Proof of Theorem tb-ax3
StepHypRef Expression
1 peirce 192 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:  re1ax2lem  31552  re1ax2  31553
  Copyright terms: Public domain W3C validator