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Metamath Proof Explorer
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 ) ) |
Proof
| 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 ) ) |