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Theorem tsxo2 34424
Description: A Tseitin axiom for logical exclusive disjunction, in deduction form. (Contributed by Giovanni Mascellani, 24-Mar-2018.)
Assertion
Ref Expression
tsxo2 (𝜃 → ((𝜑𝜓) ∨ ¬ (𝜑𝜓)))

Proof of Theorem tsxo2
StepHypRef Expression
1 tsbi2 34420 . 2 (𝜃 → ((𝜑𝜓) ∨ (𝜑𝜓)))
2 xnor 1636 . . 3 ((𝜑𝜓) ↔ ¬ (𝜑𝜓))
32orbi2i 937 . 2 (((𝜑𝜓) ∨ (𝜑𝜓)) ↔ ((𝜑𝜓) ∨ ¬ (𝜑𝜓)))
41, 3sylib 210 1 (𝜃 → ((𝜑𝜓) ∨ ¬ (𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 198  wo 874  wxo 1634
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 199  df-an 386  df-or 875  df-xor 1635
This theorem is referenced by: (None)
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