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Theorem tb-ax3 24819
Description: The third of three axioms in the Tarski-Bernays axiom system.

This axiom, along with ax-mp 8, tb-ax1 24817, and tb-ax2 24818, 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  |-  ( ( ( ph  ->  ps )  ->  ph )  ->  ph )

Proof of Theorem tb-ax3
StepHypRef Expression
1 peirce 172 1  |-  ( ( ( ph  ->  ps )  ->  ph )  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  re1ax2lem  24821  re1ax2  24822
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
  Copyright terms: Public domain W3C validator