Theorem merco1lem15 1496

Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 1478. (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 1495	. 2 ⊢ ((((φ → ψ) → ψ) → (χ → ψ)) → (φ → (χ → ψ)))
2		merco1lem13 1494	. 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)))

Syntax hints:   → wi 4

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:  merco1lem16  1497  retbwax1  1500