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Mirrors > Home > NFE Home > Th. List > mo4 | GIF version |
Description: "At most one" expressed using implicit substitution. (Contributed by NM, 26-Jul-1995.) |
Ref | Expression |
---|---|
mo4.1 | ⊢ (x = y → (φ ↔ ψ)) |
Ref | Expression |
---|---|
mo4 | ⊢ (∃*xφ ↔ ∀x∀y((φ ∧ ψ) → x = y)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1619 | . 2 ⊢ Ⅎxψ | |
2 | mo4.1 | . 2 ⊢ (x = y → (φ ↔ ψ)) | |
3 | 1, 2 | mo4f 2236 | 1 ⊢ (∃*xφ ↔ ∀x∀y((φ ∧ ψ) → x = y)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 176 ∧ wa 358 ∀wal 1540 ∃*wmo 2205 |
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 |
This theorem is referenced by: eu4 2243 rmo4 3029 dffun3 5120 dff13 5471 caovmo 5645 xpassen 6057 enpw1 6062 |
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