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Theorem merco1lem9 1690
 Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 1678. (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 1689 . 2 ((⊥ → 𝜑) → ((𝜑 → (𝜑𝜓)) → (𝜑𝜓)))
2 merco1lem8 1689 . 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 1528 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 1526  df-fal 1529 This theorem is referenced by:  merco1lem12  1693  merco1lem14  1695  merco1lem17  1698  merco1lem18  1699  retbwax1  1700
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