Description: A Tseitin axiom for logical exclusive disjunction, in deduction form. (Contributed by Giovanni Mascellani, 24-Mar-2018)
Ref | Expression | ||
---|---|---|---|
Assertion | tsxo2 | ⊢ ( 𝜃 → ( ( 𝜑 ∨ 𝜓 ) ∨ ¬ ( 𝜑 ⊻ 𝜓 ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tsbi2 | ⊢ ( 𝜃 → ( ( 𝜑 ∨ 𝜓 ) ∨ ( 𝜑 ↔ 𝜓 ) ) ) | |
2 | xnor | ⊢ ( ( 𝜑 ↔ 𝜓 ) ↔ ¬ ( 𝜑 ⊻ 𝜓 ) ) | |
3 | 2 | orbi2i | ⊢ ( ( ( 𝜑 ∨ 𝜓 ) ∨ ( 𝜑 ↔ 𝜓 ) ) ↔ ( ( 𝜑 ∨ 𝜓 ) ∨ ¬ ( 𝜑 ⊻ 𝜓 ) ) ) |
4 | 1 3 | sylib | ⊢ ( 𝜃 → ( ( 𝜑 ∨ 𝜓 ) ∨ ¬ ( 𝜑 ⊻ 𝜓 ) ) ) |