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Theorem tsan1 35572
Description: A Tseitin axiom for logical conjunction, in deduction form. (Contributed by Giovanni Mascellani, 24-Mar-2018.)
Assertion
Ref Expression
tsan1 (𝜃 → ((¬ 𝜑 ∨ ¬ 𝜓) ∨ (𝜑𝜓)))

Proof of Theorem tsan1
StepHypRef Expression
1 pm3.12 991 . 2 ((¬ 𝜑 ∨ ¬ 𝜓) ∨ (𝜑𝜓))
21a1i 11 1 (𝜃 → ((¬ 𝜑 ∨ ¬ 𝜓) ∨ (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:  tsna1  35575  ts3an1  35581  mpobi123f  35593  mptbi12f  35597
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