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Mirrors > Home > ILE Home > Th. List > rmo4f | Unicode version |
Description: Restricted "at most one" using implicit substitution. (Contributed by NM, 24-Oct-2006.) (Revised by Thierry Arnoux, 11-Oct-2016.) (Revised by Thierry Arnoux, 8-Mar-2017.) (Revised by Thierry Arnoux, 8-Oct-2017.) |
Ref | Expression |
---|---|
rmo4f.1 |
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rmo4f.2 |
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rmo4f.3 |
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rmo4f.4 |
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Ref | Expression |
---|---|
rmo4f |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rmo4f.1 |
. . 3
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2 | rmo4f.2 |
. . 3
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3 | nfv 1539 |
. . 3
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4 | 1, 2, 3 | rmo3f 2953 |
. 2
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5 | rmo4f.3 |
. . . . . 6
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6 | rmo4f.4 |
. . . . . 6
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7 | 5, 6 | sbie 1802 |
. . . . 5
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8 | 7 | anbi2i 457 |
. . . 4
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9 | 8 | imbi1i 238 |
. . 3
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10 | 9 | 2ralbii 2498 |
. 2
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11 | 4, 10 | bitri 184 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rmo 2476 |
This theorem is referenced by: disjxp1 6276 |
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