Metamath Proof Explorer

Theorem merco1lem15

Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 . (Contributed by Anthony Hart, 18-Sep-2011) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Assertion	merco1lem15	⊢ ( ( 𝜑 → 𝜓 ) → ( 𝜑 → ( 𝜒 → 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		merco1lem14	⊢ ( ( ( ( 𝜑 → 𝜓 ) → 𝜓 ) → ( 𝜒 → 𝜓 ) ) → ( 𝜑 → ( 𝜒 → 𝜓 ) ) )
2		merco1lem13	⊢ ( ( ( ( ( 𝜑 → 𝜓 ) → 𝜓 ) → ( 𝜒 → 𝜓 ) ) → ( 𝜑 → ( 𝜒 → 𝜓 ) ) ) → ( ( 𝜑 → 𝜓 ) → ( 𝜑 → ( 𝜒 → 𝜓 ) ) ) )
3	1 2	ax-mp	⊢ ( ( 𝜑 → 𝜓 ) → ( 𝜑 → ( 𝜒 → 𝜓 ) ) )