Theorem merco1lem9 1490

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
merco1lem9	⊢ ((φ → (φ → ψ)) → (φ → ψ))

Proof of Theorem merco1lem9

Step	Hyp	Ref	Expression
1		merco1lem8 1489	. 2 ⊢ (( ⊥ → φ) → ((φ → (φ → ψ)) → (φ → ψ)))
2		merco1lem8 1489	. 2 ⊢ ((( ⊥ → φ) → ((φ → (φ → ψ)) → (φ → ψ))) → ((φ → (φ → ψ)) → (φ → ψ)))
3	1, 2	ax-mp 5	1 ⊢ ((φ → (φ → ψ)) → (φ → 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:  merco1lem12  1493  merco1lem14  1495  merco1lem17  1498  merco1lem18  1499  retbwax1  1500