Theorem tbw-ax4 1736

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 36927, tb-ax2 36928, and tb-ax3 36929) 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 1587	1 ⊢ (⊥ → 𝜑)

This proof depends on syntax axioms:   → wi 4  ⊥wfal 1582

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-tru 1573  df-fal 1583

This theorem is used by:  tbwlem2  1739  tbwlem4  1741  re1luk3  1745