![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > nfeu | Structured version Visualization version GIF version |
Description: Bound-variable hypothesis builder for uniqueness. Note that 𝑥 and 𝑦 needn't be distinct. (Contributed by NM, 8-Mar-1995.) (Revised by Mario Carneiro, 7-Oct-2016.) |
Ref | Expression |
---|---|
nfeu.1 | ⊢ Ⅎ𝑥𝜑 |
Ref | Expression |
---|---|
nfeu | ⊢ Ⅎ𝑥∃!𝑦𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nftru 1843 | . . 3 ⊢ Ⅎ𝑦⊤ | |
2 | nfeu.1 | . . . 4 ⊢ Ⅎ𝑥𝜑 | |
3 | 2 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝜑) |
4 | 1, 3 | nfeud 2585 | . 2 ⊢ (⊤ → Ⅎ𝑥∃!𝑦𝜑) |
5 | 4 | trud 1606 | 1 ⊢ Ⅎ𝑥∃!𝑦𝜑 |
Colors of variables: wff setvar class |
Syntax hints: ⊤wtru 1597 Ⅎwnf 1821 ∃!weu 2571 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1835 ax-4 1850 ax-5 1952 ax-6 2018 ax-7 2054 ax-10 2132 ax-11 2147 ax-12 2160 ax-13 2355 |
This theorem depends on definitions: df-bi 197 df-or 384 df-an 385 df-tru 1599 df-ex 1818 df-nf 1823 df-eu 2575 |
This theorem is referenced by: 2eu7 2661 2eu8 2662 eusv2nf 4969 reusv2lem3 4976 bnj1489 31352 setrec2 42869 |
Copyright terms: Public domain | W3C validator |