Theorem merco1lem5 1485

Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 1478. (Contributed by Anthony Hart, 17-Sep-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

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

Proof of Theorem merco1lem5

Step	Hyp	Ref	Expression
1		merco1lem4 1484	. 2 ⊢ ((((τ → φ) → (φ → ⊥ )) → χ) → ((φ → ⊥ ) → χ))
2		merco1 1478	. 2 ⊢ (((((τ → φ) → (φ → ⊥ )) → χ) → ((φ → ⊥ ) → χ)) → ((((φ → ⊥ ) → χ) → τ) → (φ → τ)))
3	1, 2	ax-mp 5	1 ⊢ ((((φ → ⊥ ) → χ) → τ) → (φ → τ))

Syntax hints:   → wi 4   ⊥ wfal 1317

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-tru 1319  df-fal 1320

This theorem is referenced by:  merco1lem6  1486  merco1lem7  1487  merco1lem11  1492  merco1lem18  1499