Metamath Proof Explorer
Description: Formula-building rule for restricted existential quantifier (inference
form). (Contributed by NM, 16-Jun-2017)
|
|
Ref |
Expression |
|
Hypothesis |
rmobii.1 |
⊢ ( 𝜑 ↔ 𝜓 ) |
|
Assertion |
rmobii |
⊢ ( ∃* 𝑥 ∈ 𝐴 𝜑 ↔ ∃* 𝑥 ∈ 𝐴 𝜓 ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
rmobii.1 |
⊢ ( 𝜑 ↔ 𝜓 ) |
2 |
1
|
a1i |
⊢ ( 𝑥 ∈ 𝐴 → ( 𝜑 ↔ 𝜓 ) ) |
3 |
2
|
rmobiia |
⊢ ( ∃* 𝑥 ∈ 𝐴 𝜑 ↔ ∃* 𝑥 ∈ 𝐴 𝜓 ) |