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 )