Theorem tbw-ax4 1468

Description: The fourth of four axioms in the Tarski-Bernays-Wajsberg system.

This axiom was added to the Tarski-Bernays axiom system ( see tb-ax1 , tb-ax2 , and tb-ax3 in set.mm) by Wajsberg for completeness. (Contributed by Anthony Hart, 13-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
tbw-ax4	⊢ ( ⊥ → φ)

Proof of Theorem tbw-ax4

Step	Hyp	Ref	Expression
1		falim 1328	1 ⊢ ( ⊥ → φ)

Syntax hints:   → wi 4   ⊥ wfal 1317

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

This theorem depends on definitions:  df-bi 177  df-tru 1319  df-fal 1320

This theorem is referenced by:  tbwlem2  1471  tbwlem4  1473  re1luk3  1477