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Metamath Proof Explorer
Description: Inference from Theorem 19.23 of Margaris p. 90 (restricted quantifier
version). (Contributed by NM, 18-Jun-2014)
|
|
Ref |
Expression |
|
Hypothesis |
rexlimdvw.1 |
⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) |
|
Assertion |
rexlimdvw |
⊢ ( 𝜑 → ( ∃ 𝑥 ∈ 𝐴 𝜓 → 𝜒 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
rexlimdvw.1 |
⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) |
| 2 |
1
|
a1d |
⊢ ( 𝜑 → ( 𝑥 ∈ 𝐴 → ( 𝜓 → 𝜒 ) ) ) |
| 3 |
2
|
rexlimdv |
⊢ ( 𝜑 → ( ∃ 𝑥 ∈ 𝐴 𝜓 → 𝜒 ) ) |