Theorem merco1lem8

Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 . (Contributed by Anthony Hart, 17-Sep-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	merco1lem8	⊢ ( 𝜑 → ( ( 𝜓 → ( 𝜓 → 𝜒 ) ) → ( 𝜓 → 𝜒 ) ) )

Proof

Step	Hyp	Ref	Expression
1		merco1lem6	⊢ ( ( 𝜓 → ( 𝜓 → 𝜒 ) ) → ( ( 𝜓 → ( 𝜓 → 𝜒 ) ) → ( 𝜓 → 𝜒 ) ) )
2		merco1lem6	⊢ ( ( ( 𝜓 → ( 𝜓 → 𝜒 ) ) → ( ( 𝜓 → ( 𝜓 → 𝜒 ) ) → ( 𝜓 → 𝜒 ) ) ) → ( 𝜑 → ( ( 𝜓 → ( 𝜓 → 𝜒 ) ) → ( 𝜓 → 𝜒 ) ) ) )
3	1 2	ax-mp	⊢ ( 𝜑 → ( ( 𝜓 → ( 𝜓 → 𝜒 ) ) → ( 𝜓 → 𝜒 ) ) )