| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > rmobii | Structured version Visualization version GIF version | ||
| Description: Formula-building rule for restricted at-most-one quantifier (inference form). (Contributed by NM, 16-Jun-2017.) |
| Ref | Expression |
|---|---|
| rmobii.1 | ⊢ (𝜑 ↔ 𝜓) |
| Ref | Expression |
|---|---|
| rmobii | ⊢ (∃*𝑥 ∈ 𝐴 𝜑 ↔ ∃*𝑥 ∈ 𝐴 𝜓) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | rmobii.1 | . . 3 ⊢ (𝜑 ↔ 𝜓) | |
| 2 | 1 | a1i 11 | . 2 ⊢ (𝑥 ∈ 𝐴 → (𝜑 ↔ 𝜓)) |
| 3 | 2 | rmobiia 3386 | 1 ⊢ (∃*𝑥 ∈ 𝐴 𝜑 ↔ ∃*𝑥 ∈ 𝐴 𝜓) |
| Colors of variables: wff setvar class |
| Syntax hints: ↔ wb 206 ∈ wcel 2108 ∃*wrmo 3379 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1780 df-mo 2540 df-rmo 3380 |
| This theorem is referenced by: 2reu5a 3750 reuxfrd 3754 brdom7disj 10571 2sqreulem4 27498 nomaxmo 27743 reuxfrdf 32510 cvmlift2lem13 35320 ineccnvmo 38358 dfeldisj5 38722 lubeldm2 48853 glbeldm2 48854 |
| Copyright terms: Public domain | W3C validator |