Metamath Proof Explorer


Theorem tbwlem2

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
Assertion tbwlem2 φ ψ φ χ θ ψ θ

Proof

Step Hyp Ref Expression
1 tbw-ax1 φ ψ ψ χ φ χ
2 tbw-ax4 χ
3 tbw-ax1 ψ χ ψ χ
4 tbwlem1 ψ χ ψ χ χ ψ ψ χ
5 3 4 ax-mp χ ψ ψ χ
6 2 5 ax-mp ψ ψ χ
7 tbwlem1 ψ ψ χ ψ ψ χ
8 6 7 ax-mp ψ ψ χ
9 tbw-ax1 ψ ψ χ ψ χ φ χ ψ φ χ
10 8 9 ax-mp ψ χ φ χ ψ φ χ
11 1 10 tbwsyl φ ψ ψ φ χ
12 tbw-ax1 ψ φ χ φ χ θ ψ θ
13 11 12 tbwsyl φ ψ φ χ θ ψ θ