Theorem merco1lem5

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	merco1lem5	⊢ ( ( ( ( 𝜑 → ⊥ ) → 𝜒 ) → 𝜏 ) → ( 𝜑 → 𝜏 ) )

Proof

Step	Hyp	Ref	Expression
1		merco1lem4	⊢ ( ( ( ( 𝜏 → 𝜑 ) → ( 𝜑 → ⊥ ) ) → 𝜒 ) → ( ( 𝜑 → ⊥ ) → 𝜒 ) )
2		merco1	⊢ ( ( ( ( ( 𝜏 → 𝜑 ) → ( 𝜑 → ⊥ ) ) → 𝜒 ) → ( ( 𝜑 → ⊥ ) → 𝜒 ) ) → ( ( ( ( 𝜑 → ⊥ ) → 𝜒 ) → 𝜏 ) → ( 𝜑 → 𝜏 ) ) )
3	1 2	ax-mp	⊢ ( ( ( ( 𝜑 → ⊥ ) → 𝜒 ) → 𝜏 ) → ( 𝜑 → 𝜏 ) )