This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: Formula-building rule for restricted at-most-one quantifier (deduction
form). (Contributed by NM, 16-Jun-2017)
|
|
Ref |
Expression |
|
Hypothesis |
rmobidv.1 |
⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) ) |
|
Assertion |
rmobidv |
⊢ ( 𝜑 → ( ∃* 𝑥 ∈ 𝐴 𝜓 ↔ ∃* 𝑥 ∈ 𝐴 𝜒 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
rmobidv.1 |
⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) ) |
| 2 |
1
|
adantr |
⊢ ( ( 𝜑 ∧ 𝑥 ∈ 𝐴 ) → ( 𝜓 ↔ 𝜒 ) ) |
| 3 |
2
|
rmobidva |
⊢ ( 𝜑 → ( ∃* 𝑥 ∈ 𝐴 𝜓 ↔ ∃* 𝑥 ∈ 𝐴 𝜒 ) ) |