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Theorem tsxo4 34371
Description: A Tseitin axiom for logical exclusive disjunction, in deduction form. (Contributed by Giovanni Mascellani, 24-Mar-2018.)
Assertion
Ref Expression
tsxo4 (𝜃 → ((¬ 𝜑𝜓) ∨ (𝜑𝜓)))

Proof of Theorem tsxo4
StepHypRef Expression
1 tsbi4 34367 . 2 (𝜃 → ((¬ 𝜑𝜓) ∨ ¬ (𝜑𝜓)))
2 df-xor 1634 . . . 4 ((𝜑𝜓) ↔ ¬ (𝜑𝜓))
32bicomi 215 . . 3 (¬ (𝜑𝜓) ↔ (𝜑𝜓))
43orbi2i 936 . 2 (((¬ 𝜑𝜓) ∨ ¬ (𝜑𝜓)) ↔ ((¬ 𝜑𝜓) ∨ (𝜑𝜓)))
51, 4sylib 209 1 (𝜃 → ((¬ 𝜑𝜓) ∨ (𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 197  wo 873  wxo 1633
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 198  df-or 874  df-xor 1634
This theorem is referenced by: (None)
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