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Theorem re1tbw3 1820
Description: tbw-ax3 1775 rederived from merco2 1809. (Contributed by Anthony Hart, 16-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
re1tbw3 (((𝜑𝜓) → 𝜑) → 𝜑)

Proof of Theorem re1tbw3
StepHypRef Expression
1 mercolem2 1811 . 2 (((𝜑𝜑) → 𝜑) → (𝜑 → (𝜑𝜑)))
2 mercolem2 1811 . . 3 (((𝜑𝜓) → 𝜑) → ((((𝜑𝜑) → 𝜑) → (𝜑 → (𝜑𝜑))) → (((𝜑𝜓) → 𝜑) → 𝜑)))
3 mercolem6 1815 . . 3 ((((𝜑𝜓) → 𝜑) → ((((𝜑𝜑) → 𝜑) → (𝜑 → (𝜑𝜑))) → (((𝜑𝜓) → 𝜑) → 𝜑))) → ((((𝜑𝜑) → 𝜑) → (𝜑 → (𝜑𝜑))) → (((𝜑𝜓) → 𝜑) → 𝜑)))
42, 3ax-mp 5 . 2 ((((𝜑𝜑) → 𝜑) → (𝜑 → (𝜑𝜑))) → (((𝜑𝜓) → 𝜑) → 𝜑))
51, 4ax-mp 5 1 (((𝜑𝜓) → 𝜑) → 𝜑)
Colors of variables: wff setvar class
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 197  df-tru 1634  df-fal 1637
This theorem is referenced by:  re1tbw4  1821
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