Theorem merco1lem7 1487

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
merco1lem7	⊢ (φ → (((ψ → χ) → ψ) → ψ))

Proof of Theorem merco1lem7

Step	Hyp	Ref	Expression
1		merco1lem5 1485	. . 3 ⊢ ((((ψ → ⊥ ) → (((ψ → χ) → ψ) → ⊥ )) → χ) → (ψ → χ))
2		merco1 1478	. . 3 ⊢ (((((ψ → ⊥ ) → (((ψ → χ) → ψ) → ⊥ )) → χ) → (ψ → χ)) → (((ψ → χ) → ψ) → (((ψ → χ) → ψ) → ψ)))
3	1, 2	ax-mp 5	. 2 ⊢ (((ψ → χ) → ψ) → (((ψ → χ) → ψ) → ψ))
4		merco1lem6 1486	. 2 ⊢ ((((ψ → χ) → ψ) → (((ψ → χ) → ψ) → ψ)) → (φ → (((ψ → χ) → ψ) → ψ)))
5	3, 4	ax-mp 5	1 ⊢ (φ → (((ψ → χ) → ψ) → ψ))

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:  retbwax3  1488  merco1lem17  1498