Theorem merco1lem8 1489

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

Proof of Theorem merco1lem8

Step	Hyp	Ref	Expression
1		merco1lem6 1486	. 2 ⊢ ((ψ → (ψ → χ)) → ((ψ → (ψ → χ)) → (ψ → χ)))
2		merco1lem6 1486	. 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 177  df-tru 1319  df-fal 1320

This theorem is used by:  merco1lem9  1490  merco1lem14  1495