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Theorem tsxo1 34074
Description: A Tseitin axiom for logical exclusive disjunction, in deduction form. (Contributed by Giovanni Mascellani, 24-Mar-2018.)
Assertion
Ref Expression
tsxo1 (𝜃 → ((¬ 𝜑 ∨ ¬ 𝜓) ∨ ¬ (𝜑𝜓)))

Proof of Theorem tsxo1
StepHypRef Expression
1 tsbi1 34070 . 2 (𝜃 → ((¬ 𝜑 ∨ ¬ 𝜓) ∨ (𝜑𝜓)))
2 xnor 1506 . . 3 ((𝜑𝜓) ↔ ¬ (𝜑𝜓))
32orbi2i 540 . 2 (((¬ 𝜑 ∨ ¬ 𝜓) ∨ (𝜑𝜓)) ↔ ((¬ 𝜑 ∨ ¬ 𝜓) ∨ ¬ (𝜑𝜓)))
41, 3sylib 208 1 (𝜃 → ((¬ 𝜑 ∨ ¬ 𝜓) ∨ ¬ (𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 196  wo 382  wxo 1504
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-xor 1505
This theorem is referenced by: (None)
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