Metamath Proof Explorer


Theorem tbwsyl

Description: Used to rederive the Lukasiewicz axioms from Tarski-Bernays-Wajsberg'. (Contributed by Anthony Hart, 16-Aug-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses tbwsyl.1 φ ψ
tbwsyl.2 ψ χ
Assertion tbwsyl φ χ

Proof

Step Hyp Ref Expression
1 tbwsyl.1 φ ψ
2 tbwsyl.2 ψ χ
3 tbw-ax1 φ ψ ψ χ φ χ
4 1 3 ax-mp ψ χ φ χ
5 2 4 ax-mp φ χ