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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 2632 | . 2 ⊢ (∃*𝑥𝜑 → ∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) | |
2 | df-rmo 3146 | . 2 ⊢ (∃*𝑥 ∈ 𝐴 𝜑 ↔ ∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) | |
3 | 1, 2 | sylibr 236 | 1 ⊢ (∃*𝑥𝜑 → ∃*𝑥 ∈ 𝐴 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 398 ∈ wcel 2110 ∃*wmo 2616 ∃*wrmo 3141 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 |
This theorem depends on definitions: df-bi 209 df-an 399 df-ex 1777 df-mo 2618 df-rmo 3146 |
This theorem is referenced by: reueq 3727 reusv1 5289 brdom4 9946 phpreu 34870 |
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