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Mirrors > Home > MPE Home > Th. List > nfreu | Structured version Visualization version GIF version |
Description: Bound-variable hypothesis builder for restricted unique existence. (Contributed by NM, 30-Oct-2010.) (Revised by Mario Carneiro, 8-Oct-2016.) |
Ref | Expression |
---|---|
nfreu.1 | ⊢ Ⅎ𝑥𝐴 |
nfreu.2 | ⊢ Ⅎ𝑥𝜑 |
Ref | Expression |
---|---|
nfreu | ⊢ Ⅎ𝑥∃!𝑦 ∈ 𝐴 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nftru 1730 | . . 3 ⊢ Ⅎ𝑦⊤ | |
2 | nfreu.1 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
3 | 2 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝐴) |
4 | nfreu.2 | . . . 4 ⊢ Ⅎ𝑥𝜑 | |
5 | 4 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝜑) |
6 | 1, 3, 5 | nfreud 3112 | . 2 ⊢ (⊤ → Ⅎ𝑥∃!𝑦 ∈ 𝐴 𝜑) |
7 | 6 | trud 1493 | 1 ⊢ Ⅎ𝑥∃!𝑦 ∈ 𝐴 𝜑 |
Colors of variables: wff setvar class |
Syntax hints: ⊤wtru 1484 Ⅎwnf 1708 Ⅎwnfc 2751 ∃!wreu 2914 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-eu 2474 df-cleq 2615 df-clel 2618 df-nfc 2753 df-reu 2919 |
This theorem is referenced by: sbcreu 3515 reuccats1 13480 2reu7 41191 2reu8 41192 |
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