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Theorem re1tbw2 1820
Description: tbw-ax2 1775 rederived from merco2 1810. (Contributed by Anthony Hart, 16-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
re1tbw2 (𝜑 → (𝜓𝜑))

Proof of Theorem re1tbw2
StepHypRef Expression
1 mercolem1 1811 . . . 4 (((𝜑𝜑) → 𝜑) → (𝜑 → (𝜓𝜑)))
2 mercolem1 1811 . . . 4 ((((𝜑𝜑) → 𝜑) → (𝜑 → (𝜓𝜑))) → (𝜑 → (𝜓 → (𝜑 → (𝜓𝜑)))))
31, 2ax-mp 5 . . 3 (𝜑 → (𝜓 → (𝜑 → (𝜓𝜑))))
4 mercolem6 1816 . . 3 ((𝜑 → (𝜓 → (𝜑 → (𝜓𝜑)))) → (𝜓 → (𝜑 → (𝜓𝜑))))
53, 4ax-mp 5 . 2 (𝜓 → (𝜑 → (𝜓𝜑)))
6 mercolem6 1816 . 2 ((𝜓 → (𝜑 → (𝜓𝜑))) → (𝜑 → (𝜓𝜑)))
75, 6ax-mp 5 1 (𝜑 → (𝜓𝜑))
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 1635  df-fal 1638
This theorem is referenced by:  re1tbw4  1822  ltrneq  35938
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