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Mirrors > Home > NFE Home > Th. List > reurex | GIF version |
Description: Restricted unique existence implies restricted existence. (Contributed by NM, 19-Aug-1999.) |
Ref | Expression |
---|---|
reurex | ⊢ (∃!x ∈ A φ → ∃x ∈ A φ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | reu5 2824 | . 2 ⊢ (∃!x ∈ A φ ↔ (∃x ∈ A φ ∧ ∃*x ∈ A φ)) | |
2 | 1 | simplbi 446 | 1 ⊢ (∃!x ∈ A φ → ∃x ∈ A φ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∃wrex 2615 ∃!wreu 2616 ∃*wrmo 2617 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-eu 2208 df-mo 2209 df-rex 2620 df-reu 2621 df-rmo 2622 |
This theorem is referenced by: reu3 3026 |
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