Description: Nonfreeness implies the equivalent of ax5e , deduction form. (Contributed by BJ, 2-Dec-2023)
Ref | Expression | ||
---|---|---|---|
Hypothesis | bj-nnfed.1 | ⊢ ( 𝜑 → Ⅎ' 𝑥 𝜓 ) | |
Assertion | bj-nnfed | ⊢ ( 𝜑 → ( ∃ 𝑥 𝜓 → 𝜓 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-nnfed.1 | ⊢ ( 𝜑 → Ⅎ' 𝑥 𝜓 ) | |
2 | bj-nnfe | ⊢ ( Ⅎ' 𝑥 𝜓 → ( ∃ 𝑥 𝜓 → 𝜓 ) ) | |
3 | 1 2 | syl | ⊢ ( 𝜑 → ( ∃ 𝑥 𝜓 → 𝜓 ) ) |