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Theorem meran2 32106
Description: A single axiom for propositional calculus offered by Meredith. (Contributed by Anthony Hart, 13-Aug-2011.)
Assertion
Ref Expression
meran2 (¬ (¬ (¬ 𝜑𝜓) ∨ (𝜒 ∨ (𝜃𝜏))) ∨ (¬ (¬ 𝜏𝜃) ∨ (𝜒 ∨ (𝜑𝜃))))

Proof of Theorem meran2
StepHypRef Expression
1 meran1 32105 . . . 4 (¬ (¬ (¬ 𝜑𝜓) ∨ (𝜒 ∨ (𝜃𝜏))) ∨ (¬ (¬ 𝜃𝜑) ∨ (𝜒 ∨ (𝜏𝜑))))
21imorri 430 . . 3 ((¬ (¬ 𝜑𝜓) ∨ (𝜒 ∨ (𝜃𝜏))) → (¬ (¬ 𝜃𝜑) ∨ (𝜒 ∨ (𝜏𝜑))))
3 meran1 32105 . . . 4 (¬ (¬ (¬ 𝜃𝜑) ∨ (𝜒 ∨ (𝜏𝜑))) ∨ (¬ (¬ 𝜏𝜃) ∨ (𝜒 ∨ (𝜑𝜃))))
43imorri 430 . . 3 ((¬ (¬ 𝜃𝜑) ∨ (𝜒 ∨ (𝜏𝜑))) → (¬ (¬ 𝜏𝜃) ∨ (𝜒 ∨ (𝜑𝜃))))
52, 4syl 17 . 2 ((¬ (¬ 𝜑𝜓) ∨ (𝜒 ∨ (𝜃𝜏))) → (¬ (¬ 𝜏𝜃) ∨ (𝜒 ∨ (𝜑𝜃))))
65imori 429 1 (¬ (¬ (¬ 𝜑𝜓) ∨ (𝜒 ∨ (𝜃𝜏))) ∨ (¬ (¬ 𝜏𝜃) ∨ (𝜒 ∨ (𝜑𝜃))))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wo 383
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-or 385
This theorem is referenced by: (None)
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