Description: Deduction associated with nfnt . (Contributed by Mario Carneiro, 24-Sep-2016)
Ref | Expression | ||
---|---|---|---|
Hypothesis | nfnd.1 | ⊢ ( 𝜑 → Ⅎ 𝑥 𝜓 ) | |
Assertion | nfnd | ⊢ ( 𝜑 → Ⅎ 𝑥 ¬ 𝜓 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfnd.1 | ⊢ ( 𝜑 → Ⅎ 𝑥 𝜓 ) | |
2 | nfnt | ⊢ ( Ⅎ 𝑥 𝜓 → Ⅎ 𝑥 ¬ 𝜓 ) | |
3 | 1 2 | syl | ⊢ ( 𝜑 → Ⅎ 𝑥 ¬ 𝜓 ) |