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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 1395 | . . 3 ⊢ Ⅎ𝑦⊤ | |
2 | nfeu.1 | . . . 4 ⊢ Ⅎ𝑥𝜑 | |
3 | 2 | a1i 9 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝜑) |
4 | 1, 3 | nfmod 1958 | . 2 ⊢ (⊤ → Ⅎ𝑥∃*𝑦𝜑) |
5 | 4 | trud 1293 | 1 ⊢ Ⅎ𝑥∃*𝑦𝜑 |
Colors of variables: wff set class |
Syntax hints: ⊤wtru 1285 Ⅎwnf 1389 ∃*wmo 1942 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 |
This theorem is referenced by: euexex 2026 nfdisjv 3778 reusv1 4208 mosubopt 4423 dffun6f 4935 |
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