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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 2512 | . 2 ⊢ (∃*𝑥𝜑 → ∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) | |
2 | df-rmo 2904 | . 2 ⊢ (∃*𝑥 ∈ 𝐴 𝜑 ↔ ∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) | |
3 | 1, 2 | sylibr 223 | 1 ⊢ (∃*𝑥𝜑 → ∃*𝑥 ∈ 𝐴 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 ∈ wcel 1977 ∃*wmo 2459 ∃*wrmo 2899 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-12 2034 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-eu 2462 df-mo 2463 df-rmo 2904 |
This theorem is referenced by: reueq 3371 reusv1 4792 reusv1OLD 4793 brdom4 9233 phpreu 32563 |
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