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Mirrors > Home > ILE Home > Th. List > mormo | 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 2066 | . 2 ⊢ (∃*𝑥𝜑 → ∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) | |
2 | df-rmo 2422 | . 2 ⊢ (∃*𝑥 ∈ 𝐴 𝜑 ↔ ∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) | |
3 | 1, 2 | sylibr 133 | 1 ⊢ (∃*𝑥𝜑 → ∃*𝑥 ∈ 𝐴 𝜑) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 103 ∈ wcel 1480 ∃*wmo 1998 ∃*wrmo 2417 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-rmo 2422 |
This theorem is referenced by: reueq 2878 reusv1 4374 |
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