Theorem tbw-ax4 1704

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 33733, tb-ax2 33734, and tb-ax3 33735) 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 1554	1 ⊢ (⊥ → 𝜑)

Syntax hints:   → wi 4  ⊥wfal 1549

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 209  df-tru 1540  df-fal 1550

This theorem is referenced by:  tbwlem2  1707  tbwlem4  1709  re1luk3  1713