Theorem merco1lem8 1753

Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 1742. (Contributed by Anthony Hart, 17-Sep-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

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

Proof of Theorem merco1lem8

Step	Hyp	Ref	Expression
1		merco1lem6 1750	. 2 ⊢ ((𝜓 → (𝜓 → 𝜒)) → ((𝜓 → (𝜓 → 𝜒)) → (𝜓 → 𝜒)))
2		merco1lem6 1750	. 2 ⊢ (((𝜓 → (𝜓 → 𝜒)) → ((𝜓 → (𝜓 → 𝜒)) → (𝜓 → 𝜒))) → (𝜑 → ((𝜓 → (𝜓 → 𝜒)) → (𝜓 → 𝜒))))
3	1, 2	ax-mp 5	1 ⊢ (𝜑 → ((𝜓 → (𝜓 → 𝜒)) → (𝜓 → 𝜒)))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-tru 1572  df-fal 1582

This theorem is used by:  merco1lem9  1754  merco1lem14  1759