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| Mirrors > Home > MPE Home > Th. List > mormo | Structured version Visualization version GIF version | ||
| Description: Unrestricted "at most one" implies restricted "at most one". (Contributed by NM, 16-Jun-2017.) | 
| Ref | Expression | 
|---|---|
| mormo | ⊢ (∃*𝑥𝜑 → ∃*𝑥 ∈ 𝐴 𝜑) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | moan 2551 | . 2 ⊢ (∃*𝑥𝜑 → ∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) | |
| 2 | df-rmo 3379 | . 2 ⊢ (∃*𝑥 ∈ 𝐴 𝜑 ↔ ∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) | |
| 3 | 1, 2 | sylibr 234 | 1 ⊢ (∃*𝑥𝜑 → ∃*𝑥 ∈ 𝐴 𝜑) | 
| Colors of variables: wff setvar class | 
| Syntax hints: → wi 4 ∧ wa 395 ∈ wcel 2107 ∃*wmo 2537 ∃*wrmo 3378 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1794 ax-4 1808 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1779 df-mo 2539 df-rmo 3379 | 
| This theorem is referenced by: reueq 3742 reusv1 5396 brdom4 10571 phpreu 37612 | 
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