Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > nfmo | GIF version |
Description: Bound-variable hypothesis builder for "at most one". (Contributed by NM, 9-Mar-1995.) |
Ref | Expression |
---|---|
nfeu.1 | ⊢ Ⅎ𝑥𝜑 |
Ref | Expression |
---|---|
nfmo | ⊢ Ⅎ𝑥∃*𝑦𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nftru 1459 | . . 3 ⊢ Ⅎ𝑦⊤ | |
2 | nfeu.1 | . . . 4 ⊢ Ⅎ𝑥𝜑 | |
3 | 2 | a1i 9 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝜑) |
4 | 1, 3 | nfmod 2036 | . 2 ⊢ (⊤ → Ⅎ𝑥∃*𝑦𝜑) |
5 | 4 | mptru 1357 | 1 ⊢ Ⅎ𝑥∃*𝑦𝜑 |
Colors of variables: wff set class |
Syntax hints: ⊤wtru 1349 Ⅎwnf 1453 ∃*wmo 2020 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 |
This theorem is referenced by: euexex 2104 nfdisjv 3978 reusv1 4443 mosubopt 4676 dffun6f 5211 |
Copyright terms: Public domain | W3C validator |