Theorem tsxo2 38815

Description: A Tseitin axiom for logical exclusive disjunction, in deduction form. (Contributed by Giovanni Mascellani, 24-Mar-2018.)

Assertion

Ref	Expression
tsxo2	⊢ (𝜃 → ((𝜑 ∨ 𝜓) ∨ ¬ (𝜑 ⊻ 𝜓)))

Proof of Theorem tsxo2

Step	Hyp	Ref	Expression
1		tsbi2 38811	. 2 ⊢ (𝜃 → ((𝜑 ∨ 𝜓) ∨ (𝜑 ↔ 𝜓)))
2		xnor 1542	. . 3 ⊢ ((𝜑 ↔ 𝜓) ↔ ¬ (𝜑 ⊻ 𝜓))
3	2	orbi2i 925	. 2 ⊢ (((𝜑 ∨ 𝜓) ∨ (𝜑 ↔ 𝜓)) ↔ ((𝜑 ∨ 𝜓) ∨ ¬ (𝜑 ⊻ 𝜓)))
4	1, 3	sylib 221	1 ⊢ (𝜃 → ((𝜑 ∨ 𝜓) ∨ ¬ (𝜑 ⊻ 𝜓)))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ↔ wb 209   ∨ wo 860   ⊻ wxo 1540

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 401  df-or 861  df-xor 1541

This theorem is used by: (None)