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Theorem tsna2 34082
Description: A Tseitin axiom for logical incompatibility, in deduction form. (Contributed by Giovanni Mascellani, 24-Mar-2018.)
Assertion
Ref Expression
tsna2 (𝜃 → (𝜑 ∨ (𝜑𝜓)))

Proof of Theorem tsna2
StepHypRef Expression
1 tsan2 34079 . 2 (𝜃 → (𝜑 ∨ ¬ (𝜑𝜓)))
2 df-nan 1488 . . 3 ((𝜑𝜓) ↔ ¬ (𝜑𝜓))
32orbi2i 540 . 2 ((𝜑 ∨ (𝜑𝜓)) ↔ (𝜑 ∨ ¬ (𝜑𝜓)))
41, 3sylibr 224 1 (𝜃 → (𝜑 ∨ (𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wo 382  wa 383  wnan 1487
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 384  df-an 385  df-nan 1488
This theorem is referenced by: (None)
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