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Database CLASSICAL FIRST-ORDER LOGIC WITH EQUALITY Other axiomatizations related to classical propositional calculus Derive the Lukasiewicz Axioms from the Tarski-Bernays-Wajsberg Axioms 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 )