Description: A Tseitin axiom for logical incompatibility, in deduction form. (Contributed by Giovanni Mascellani, 24-Mar-2018)
Ref | Expression | ||
---|---|---|---|
Assertion | tsna3 | ⊢ ( 𝜃 → ( 𝜓 ∨ ( 𝜑 ⊼ 𝜓 ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tsan3 | ⊢ ( 𝜃 → ( 𝜓 ∨ ¬ ( 𝜑 ∧ 𝜓 ) ) ) | |
2 | df-nan | ⊢ ( ( 𝜑 ⊼ 𝜓 ) ↔ ¬ ( 𝜑 ∧ 𝜓 ) ) | |
3 | 2 | orbi2i | ⊢ ( ( 𝜓 ∨ ( 𝜑 ⊼ 𝜓 ) ) ↔ ( 𝜓 ∨ ¬ ( 𝜑 ∧ 𝜓 ) ) ) |
4 | 1 3 | sylibr | ⊢ ( 𝜃 → ( 𝜓 ∨ ( 𝜑 ⊼ 𝜓 ) ) ) |