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Mirrors > Home > NFE Home > Th. List > nfmod2 | GIF version |
Description: Bound-variable hypothesis builder for uniqueness. (Contributed by Mario Carneiro, 14-Nov-2016.) |
Ref | Expression |
---|---|
nfeud2.1 | ⊢ Ⅎyφ |
nfeud2.2 | ⊢ ((φ ∧ ¬ ∀x x = y) → Ⅎxψ) |
Ref | Expression |
---|---|
nfmod2 | ⊢ (φ → Ⅎx∃*yψ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-mo 2209 | . 2 ⊢ (∃*yψ ↔ (∃yψ → ∃!yψ)) | |
2 | nfeud2.1 | . . . 4 ⊢ Ⅎyφ | |
3 | nfeud2.2 | . . . 4 ⊢ ((φ ∧ ¬ ∀x x = y) → Ⅎxψ) | |
4 | 2, 3 | nfexd2 1973 | . . 3 ⊢ (φ → Ⅎx∃yψ) |
5 | 2, 3 | nfeud2 2216 | . . 3 ⊢ (φ → Ⅎx∃!yψ) |
6 | 4, 5 | nfimd 1808 | . 2 ⊢ (φ → Ⅎx(∃yψ → ∃!yψ)) |
7 | 1, 6 | nfxfrd 1571 | 1 ⊢ (φ → Ⅎx∃*yψ) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∧ wa 358 ∀wal 1540 ∃wex 1541 Ⅎwnf 1544 ∃!weu 2204 ∃*wmo 2205 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 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-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-eu 2208 df-mo 2209 |
This theorem is referenced by: nfmod 2219 nfrmod 2784 nfrmo 2786 |
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