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Metamath Proof Explorer
Description: Inference associated with 19.37v . (Contributed by NM, 5-Aug-1993)
Remove dependency on ax-6 . (Revised by Rohan Ridenour, 15-Apr-2022)
|
|
Ref |
Expression |
|
Hypothesis |
19.37iv.1 |
⊢ ∃ 𝑥 ( 𝜑 → 𝜓 ) |
|
Assertion |
19.37iv |
⊢ ( 𝜑 → ∃ 𝑥 𝜓 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
19.37iv.1 |
⊢ ∃ 𝑥 ( 𝜑 → 𝜓 ) |
| 2 |
|
19.37imv |
⊢ ( ∃ 𝑥 ( 𝜑 → 𝜓 ) → ( 𝜑 → ∃ 𝑥 𝜓 ) ) |
| 3 |
1 2
|
ax-mp |
⊢ ( 𝜑 → ∃ 𝑥 𝜓 ) |