Theorem merco1lem15 1760

Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 1742. (Contributed by Anthony Hart, 18-Sep-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

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

Proof of Theorem merco1lem15

Step	Hyp	Ref	Expression
1		merco1lem14 1759	. 2 ⊢ ((((𝜑 → 𝜓) → 𝜓) → (𝜒 → 𝜓)) → (𝜑 → (𝜒 → 𝜓)))
2		merco1lem13 1758	. 2 ⊢ (((((𝜑 → 𝜓) → 𝜓) → (𝜒 → 𝜓)) → (𝜑 → (𝜒 → 𝜓))) → ((𝜑 → 𝜓) → (𝜑 → (𝜒 → 𝜓))))
3	1, 2	ax-mp 5	1 ⊢ ((𝜑 → 𝜓) → (𝜑 → (𝜒 → 𝜓)))

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:  merco1lem16  1761  retbwax1  1764