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Mirrors > Home > ILE Home > Th. List > funcnv3 | Unicode version |
Description: A condition showing a class is single-rooted. (See funcnv 5279). (Contributed by NM, 26-May-2006.) |
Ref | Expression |
---|---|
funcnv3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfrn2 4817 |
. . . . . 6
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2 | 1 | abeq2i 2288 |
. . . . 5
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3 | 2 | biimpi 120 |
. . . 4
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4 | 3 | biantrurd 305 |
. . 3
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5 | 4 | ralbiia 2491 |
. 2
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6 | funcnv 5279 |
. 2
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7 | df-reu 2462 |
. . . 4
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8 | vex 2742 |
. . . . . . 7
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9 | vex 2742 |
. . . . . . 7
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10 | 8, 9 | breldm 4833 |
. . . . . 6
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11 | 10 | pm4.71ri 392 |
. . . . 5
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12 | 11 | eubii 2035 |
. . . 4
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13 | eu5 2073 |
. . . 4
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14 | 7, 12, 13 | 3bitr2i 208 |
. . 3
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15 | 14 | ralbii 2483 |
. 2
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16 | 5, 6, 15 | 3bitr4i 212 |
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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-sep 4123 ax-pow 4176 ax-pr 4211 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-reu 2462 df-v 2741 df-un 3135 df-in 3137 df-ss 3144 df-pw 3579 df-sn 3600 df-pr 3601 df-op 3603 df-br 4006 df-opab 4067 df-id 4295 df-xp 4634 df-rel 4635 df-cnv 4636 df-co 4637 df-dm 4638 df-rn 4639 df-fun 5220 |
This theorem is referenced by: (None) |
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