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Theorem tsan2 35573
Description: A Tseitin axiom for logical conjunction, in deduction form. (Contributed by Giovanni Mascellani, 24-Mar-2018.)
Assertion
Ref Expression
tsan2 (𝜃 → (𝜑 ∨ ¬ (𝜑𝜓)))

Proof of Theorem tsan2
StepHypRef Expression
1 pm3.14 993 . . . 4 ((¬ 𝜑 ∨ ¬ 𝜓) → ¬ (𝜑𝜓))
21orcs 872 . . 3 𝜑 → ¬ (𝜑𝜓))
32orri 859 . 2 (𝜑 ∨ ¬ (𝜑𝜓))
43a1i 11 1 (𝜃 → (𝜑 ∨ ¬ (𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wa 399  wo 844
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-an 400  df-or 845
This theorem is referenced by:  tsna2  35576  ts3an2  35582  mpobi123f  35593  mptbi12f  35597
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