Theorem re1tbw3 1512

Description: tbw-ax3 1467 rederived from merco2 1501. (Contributed by Anthony Hart, 16-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
re1tbw3	⊢ (((φ → ψ) → φ) → φ)

Proof of Theorem re1tbw3

Step	Hyp	Ref	Expression
1		mercolem2 1503	. 2 ⊢ (((φ → φ) → φ) → (φ → (φ → φ)))
2		mercolem2 1503	. . 3 ⊢ (((φ → ψ) → φ) → ((((φ → φ) → φ) → (φ → (φ → φ))) → (((φ → ψ) → φ) → φ)))
3		mercolem6 1507	. . 3 ⊢ ((((φ → ψ) → φ) → ((((φ → φ) → φ) → (φ → (φ → φ))) → (((φ → ψ) → φ) → φ))) → ((((φ → φ) → φ) → (φ → (φ → φ))) → (((φ → ψ) → φ) → φ)))
4	2, 3	ax-mp 5	. 2 ⊢ ((((φ → φ) → φ) → (φ → (φ → φ))) → (((φ → ψ) → φ) → φ))
5	1, 4	ax-mp 5	1 ⊢ (((φ → ψ) → φ) → φ)

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:  re1tbw4  1513