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Mirrors > Home > ILE Home > Th. List > ssrmof | Unicode version |
Description: "At most one" existential quantification restricted to a subclass. (Contributed by Thierry Arnoux, 8-Oct-2017.) |
Ref | Expression |
---|---|
ssrexf.1 | |
ssrexf.2 |
Ref | Expression |
---|---|
ssrmof |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssrexf.1 | . . . . 5 | |
2 | ssrexf.2 | . . . . 5 | |
3 | 1, 2 | dfss2f 3088 | . . . 4 |
4 | 3 | biimpi 119 | . . 3 |
5 | pm3.45 586 | . . . 4 | |
6 | 5 | alimi 1431 | . . 3 |
7 | moim 2063 | . . 3 | |
8 | 4, 6, 7 | 3syl 17 | . 2 |
9 | df-rmo 2424 | . 2 | |
10 | df-rmo 2424 | . 2 | |
11 | 8, 9, 10 | 3imtr4g 204 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wal 1329 wcel 1480 wmo 2000 wnfc 2268 wrmo 2419 wss 3071 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-rmo 2424 df-in 3077 df-ss 3084 |
This theorem is referenced by: (None) |
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