Theorem retbwax3 1639

Description: tbw-ax3 1618 rederived from merco1 1629. (Contributed by Anthony Hart, 17-Sep-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
retbwax3	⊢ (((𝜑 → 𝜓) → 𝜑) → 𝜑)

Proof of Theorem retbwax3

Step	Hyp	Ref	Expression
1		retbwax2 1632	. 2 ⊢ (𝜑 → (𝜑 → 𝜑))
2		merco1lem7 1638	. 2 ⊢ ((𝜑 → (𝜑 → 𝜑)) → (((𝜑 → 𝜓) → 𝜑) → 𝜑))
3	1, 2	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 196  df-tru 1478  df-fal 1481

This theorem is referenced by: (None)