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Theorem merco1lem9 1733
Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 1721. (Contributed by Anthony Hart, 18-Sep-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
merco1lem9 ((𝜑 → (𝜑𝜓)) → (𝜑𝜓))

Proof of Theorem merco1lem9
StepHypRef Expression
1 merco1lem8 1732 . 2 ((⊥ → 𝜑) → ((𝜑 → (𝜑𝜓)) → (𝜑𝜓)))
2 merco1lem8 1732 . 2 (((⊥ → 𝜑) → ((𝜑 → (𝜑𝜓)) → (𝜑𝜓))) → ((𝜑 → (𝜑𝜓)) → (𝜑𝜓)))
31, 2ax-mp 5 1 ((𝜑 → (𝜑𝜓)) → (𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wfal 1555
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 210  df-tru 1546  df-fal 1556
This theorem is referenced by:  merco1lem12  1736  merco1lem14  1738  merco1lem17  1741  merco1lem18  1742  retbwax1  1743
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