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Mirrors > Home > ILE Home > Th. List > nfmo1 | GIF version |
Description: Bound-variable hypothesis builder for "at most one." (Contributed by NM, 8-Mar-1995.) (Revised by Mario Carneiro, 7-Oct-2016.) |
Ref | Expression |
---|---|
nfmo1 | ⊢ Ⅎ𝑥∃*𝑥𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-mo 2004 | . 2 ⊢ (∃*𝑥𝜑 ↔ (∃𝑥𝜑 → ∃!𝑥𝜑)) | |
2 | nfe1 1473 | . . 3 ⊢ Ⅎ𝑥∃𝑥𝜑 | |
3 | nfeu1 2011 | . . 3 ⊢ Ⅎ𝑥∃!𝑥𝜑 | |
4 | 2, 3 | nfim 1552 | . 2 ⊢ Ⅎ𝑥(∃𝑥𝜑 → ∃!𝑥𝜑) |
5 | 1, 4 | nfxfr 1451 | 1 ⊢ Ⅎ𝑥∃*𝑥𝜑 |
Colors of variables: wff set class |
Syntax hints: → wi 4 Ⅎwnf 1437 ∃wex 1469 ∃!weu 2000 ∃*wmo 2001 |
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-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-4 1488 ax-ial 1515 ax-i5r 1516 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-eu 2003 df-mo 2004 |
This theorem is referenced by: moanmo 2077 euexex 2085 nfrmo1 2606 mob 2870 morex 2872 funimaexglem 5214 |
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