Theorem re1tbw2 1511

Description: tbw-ax2 1466 rederived from merco2 1501. (Contributed by Anthony Hart, 16-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
re1tbw2	⊢ (φ → (ψ → φ))

Proof of Theorem re1tbw2

Step	Hyp	Ref	Expression
1		mercolem1 1502	. . . 4 ⊢ (((φ → φ) → φ) → (φ → (ψ → φ)))
2		mercolem1 1502	. . . 4 ⊢ ((((φ → φ) → φ) → (φ → (ψ → φ))) → (φ → (ψ → (φ → (ψ → φ)))))
3	1, 2	ax-mp 5	. . 3 ⊢ (φ → (ψ → (φ → (ψ → φ))))
4		mercolem6 1507	. . 3 ⊢ ((φ → (ψ → (φ → (ψ → φ)))) → (ψ → (φ → (ψ → φ))))
5	3, 4	ax-mp 5	. 2 ⊢ (ψ → (φ → (ψ → φ)))
6		mercolem6 1507	. 2 ⊢ ((ψ → (φ → (ψ → φ))) → (φ → (ψ → φ)))
7	5, 6	ax-mp 5	1 ⊢ (φ → (ψ → φ))

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:  re1tbw4  1513