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Theorem merco1lem5 1764
 Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 1757. (Contributed by Anthony Hart, 17-Sep-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
merco1lem5 ((((𝜑 → ⊥) → 𝜒) → 𝜏) → (𝜑𝜏))

Proof of Theorem merco1lem5
StepHypRef Expression
1 merco1lem4 1763 . 2 ((((𝜏𝜑) → (𝜑 → ⊥)) → 𝜒) → ((𝜑 → ⊥) → 𝜒))
2 merco1 1757 . 2 (((((𝜏𝜑) → (𝜑 → ⊥)) → 𝜒) → ((𝜑 → ⊥) → 𝜒)) → ((((𝜑 → ⊥) → 𝜒) → 𝜏) → (𝜑𝜏)))
31, 2ax-mp 5 1 ((((𝜑 → ⊥) → 𝜒) → 𝜏) → (𝜑𝜏))
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ⊥wfal 1614 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 199  df-tru 1605  df-fal 1615 This theorem is referenced by:  merco1lem6  1765  merco1lem7  1766  merco1lem11  1771  merco1lem18  1778
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