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Theorem tsxo3 33116
 Description: A Tseitin axiom for logical exclusive disjunction, in deduction form. (Contributed by Giovanni Mascellani, 24-Mar-2018.)
Assertion
Ref Expression
tsxo3 (𝜃 → ((𝜑 ∨ ¬ 𝜓) ∨ (𝜑𝜓)))

Proof of Theorem tsxo3
StepHypRef Expression
1 tsbi3 33112 . 2 (𝜃 → ((𝜑 ∨ ¬ 𝜓) ∨ ¬ (𝜑𝜓)))
2 df-xor 1457 . . . 4 ((𝜑𝜓) ↔ ¬ (𝜑𝜓))
32bicomi 213 . . 3 (¬ (𝜑𝜓) ↔ (𝜑𝜓))
43orbi2i 540 . 2 (((𝜑 ∨ ¬ 𝜓) ∨ ¬ (𝜑𝜓)) ↔ ((𝜑 ∨ ¬ 𝜓) ∨ (𝜑𝜓)))
51, 4sylib 207 1 (𝜃 → ((𝜑 ∨ ¬ 𝜓) ∨ (𝜑𝜓)))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 195   ∨ wo 382   ⊻ wxo 1456 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 196  df-or 384  df-xor 1457 This theorem is referenced by: (None)
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